What is identities: Definition and 422 Discussions

In trigonometry, trigonometric identities are equalities that involve trigonometric functions and are true for every value of the occurring variables for which both sides of the equality are defined. Geometrically, these are identities involving certain functions of one or more angles. They are distinct from triangle identities, which are identities potentially involving angles but also involving side lengths or other lengths of a triangle.
These identities are useful whenever expressions involving trigonometric functions need to be simplified. An important application is the integration of non-trigonometric functions: a common technique involves first using the substitution rule with a trigonometric function, and then simplifying the resulting integral with a trigonometric identity.

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  1. A

    Question involving trigonometric identities and inverse functions

    [SOLVED] Question involving trigonometric identities and inverse functions Homework Statement http://img141.imageshack.us/img141/2651/quiz1question5zi8.jpg Homework Equations I've tried to combine the following known equations to come up with a solution: \frac{d}{dx}(sin^{-1}x) =...
  2. F

    Verifying Trigonometric Identities

    First I wanted to say hello, that I'm new to the forum, and very glad to have found you! I am having a terrific time with verifying my trig identities. I have done ALL odd probs in my text, and am repeating them. The problem that I am having is that I do not see a clear path from one side of...
  3. R

    Problem Verifing Identities in Trig

    Hello this one has stumped me for about a day and I have tried several different approaches. maybe someone could point me in the right direction. cot^2x-1/1+cot^2x=2Cos^2x-1 I startedon the Left side tring to prove the equation. cot^2x-1/csc^2x using Pyth. Theory...
  4. A

    Cos^2 - Sin^2 = Cos(2a): Shaum's Solution

    Anyone know if the difference of cos^2 and sin^2 is some obscure identity that no one's heard of? Edit: nevermind. Shaum's tells me that cos^2 - sin^2 = cos(2a). GO SHAUMS!
  5. N

    Vector Identities: Calculate & Surface Integrals

    Homework Statement 1. Calculate: \nabla \times (\frac{\vec{p} \times \vec{r}}{r^{3}}) in cartesian and spherical coordinates, where \vec{p} is a constant vector. 2. Calculate surface integrals: \int \vec{r} (\vec{a} \cdot \vec{n}) dS \int \vec{n} (\vec{a} \cdot \vec{r}) dS where...
  6. J

    Trig Without Tears - Tutorials To Help You Develop Identities

    http://oakroadsystems.com/twt/ I searched and it looked like no one had posted this before, so here it is. Trig without tears is an awesome site in which some guy explains trigonometry, from the basic functions of sine and cosine to the double and half angle identities. The interesting part...
  7. K

    Is This Trigonometric Identity Solvable?

    [SOLVED] Proving Trig Identities Homework Statement Prove that tanx - sinx---=---- tanxsinx ________------- _________ tanxsinx -------- tanx + sinx Homework Equations Is this impossible, so far it has been for me, what about you? The Attempt at a Solution I...
  8. V

    Few questions on proving identities

    Homework Statement seca + csca --------------- = seca*csca sina + cosa Homework Equations no relevant equations The Attempt at a Solution How would i prove this ?? i know i break down the left side... which is 1/cosa + 1/sina --------------------- sina + cosa
  9. M

    Solve X in 4.59 x 10^-4 = Sin^3(x)/Cos(x)

    Homework Statement 4.59 x 10^-4 = Sin^3(x)/Cos(x) Solve for XHomework Equations Sin(x)/Cos(x) = Tan(x) The Attempt at a Solution We can make Sin^3(x)/Cos(x) into Tan(x)Sin^2(x), but I don't think that helps... What trick do I use?
  10. haushofer

    Geodesic coordinates and tensor identities

    Hi, I have a question about deriving tensor identities using geodesic coordinates ( coordinates in which one can put the connection to zero ). For the reference, I'm a master student physics and followed courses on general relativity and geometry. I'm busy with an article of Wald and Lee called...
  11. J

    How Do Double Angle Identities Simplify Trigonometric Equations?

    Homework Statement sin4x-sin2x/sin2x=cos3x/cosx Homework Equations sin2x = 2sinxcosx The Attempt at a Solution LS = sin(2x + 2x) - sin2x/sin2x = sin2xcos2x + cos2xsin2x - sin2x/sin2x = 2sin2xcos2x - sin2x/sin2x This is where i get stuck... I don't know what happens if you try...
  12. R

    Trig Identities and Double Angle Formulas

    [SOLVED] Trig Identities and Double Angle Formulas Homework Statement If tan(a) = 1/5 and tan(b) = 1/239, find tan(4a - b) Homework Equations tan2x = 2tanx/1-tan^2x tan(x-y) = tanx - tany/ 1 +tanx tany The Attempt at a Solution tan (4a - b) = (tan4a - tanb)/(1 + tan4a tanb)...
  13. rocomath

    Are these trig identities correct?

    cos(90+theta) = sin(theta) sin(90+theta) = -cos(theta) cos is negative in 2nd quad sin is positive in 2nd quad i'm looking at some soln's and i just need clarification, thanks!
  14. C

    Identities for covariant derivative

    Hi. I'm considering the covariant derivative \nabla_\mu V^\nu = \partial_\mu V^\nu + \Gamma_{\mu\nu}^\lambda V^\lambda in spherical coordinates in flat 3D space (x = r cos sin, y = r sin sin, z = r cos; usual stuff). Now I wrote down the gradient of a scalar function f, for which I got...
  15. T

    Understanding Trig Identities: Sum and Diff. & Multiple Angle

    can anyone help me understand the following and how to apply them: tig identities sum and diff. indentities multiple angle indentities I'd really appreciate it. Thanx
  16. A

    Proving Product-to-Sum Identities: Need help

    Homework Statement Prove the following product-to-sum identities: i) cosucosv = 1/2[cos(u + v)+cos(u - v)] ii) sinusinv = 1/2[cos(u - v) - cos(u + v)] Any help/hints would be appreciated. The TAs (teacher assistants) can't help us with our problem set questions, so I'm stuck on this...
  17. J

    Mechanics/Projectiles/Angles/Trig. Identities?

    Homework Statement http://img213.imageshack.us/img213/1681/question1su9.png Apologies for the scrappy diagram. My MS Paint skills aren't amazing.Homework Equations Personally, I'm not too sure. This question (I think) involves things that I haven't studied, I tried to do a little research...
  18. E

    Where Can I Find a Large Trig Identities Poster for My Dorm?

    Does anyone know where I can get a nice large trig identities poster that I can put up in my dorm so I don't always have to look through wikipedia?
  19. Saladsamurai

    Proving Cosine Identity: Is cos(t+2π) the Same as cos(t)?

    \cos (t)=\cos(t+2\pi) I know it is kind of silly, but I need to do it. I could have sworn that a sum formula would have worked, ie., \cos(\alpha+\beta)=\cos \alpha \cos \beta -\sin \alpha \sin \beta but when I sub in t and 2\pi for the RHS, I am getting -\cos t Where did I go wrong...
  20. T

    Using Trig Identities to Simplify Sin(Kx)sin(2Kx)

    Could someone tell me which trig identity this chap (in a Physics textbook) is using to turn sin(Kx)sin(2Kx) into sin^2(3Kx/2) - sin^2(Kx/2) Cheers.
  21. J

    Proving the Identity: cot x + tan x = sec x csc x

    I need to prove algebraically this and I'm having trouble with it. cot x + tan x = sec x csc x Can anyone help me?
  22. W

    Trigonometrical Identities and Simple Equations

    Hi there, I am struggling with trigonometrical identities and how to use them effectively. I can work out simpler problems but I can't seem to get my head round slightly bigger ones like this:- Simplify:- sin^4(x) + 2sin^2(x)cos^2(x) + cos^4(x) I 've tried substituting...
  23. J

    Converting Complex Numbers to Trigonometric Identities

    I was never good at trigonometric identities. Let z= cos x + i sin x Express 2/(1 + z) in the form 1 - i tan kx I need help. A pointer to where to start would be great.
  24. D

    Prove sum identities: r</=>1, θ, e^iθ

    Homework Statement Prove the following identities: \sum_{n=0}^{\infty} r^n \cos(n\theta) = \frac{1-r\cos(\theta)}{1-2r\cos(\theta)+r^2} \sum_{n=0}^{\infty} r^n \sin(n\theta) = \frac{r\sin(\theta)}{1-2r\cos(\theta)+r^2} Homework Equations \cos(n\theta) =...
  25. M

    Help Finding Values of Cosx & Sinx | tanx=2

    Can someone kindly help to find the exact values of cosx and sinx when tanx=2..:redface:
  26. D

    Having trouble solving Sin2x-1=0? Let's tackle it together!

    Ok this is my first post...so bear with me :smile: My problem is: Sin2x-1=0 I thought I recognized that Sin2x is from the double angle identities chapter so I substituted [2CosSin] for Sin2x. So I ended up with 2CosSin=1 ( I moved the one over) ...and then I got stuck... am I...
  27. D

    Hypergeometric transformations and identities

    How do you derive hypergeometirc identities of the form 2F1(a,b,c,z)= gamma function. What I mean is that the hypergeometric function converges to a set of gamme functions function in terms of (a,b,c) where z is not 1,-1, or 1/2 ? The hypergeometric identities in the mathworld summary...
  28. N

    Help with proving identities please

    i need help with proving these identities 1/sinxcosx - cosx/sinx= tanx 1/1+cosx=csc^2x-cscxcotx sinx/1-cosx + 1_cosx/sinx = 2cscx i would really appreciate this
  29. X

    Can you help me solve this trig identity question?

    hey guyz...ok iv been trying to figure this question out for so long...and i jus can't.i get up to a certain point and then i jus get confused.so if anyone can help me that would be great! Prov that: Cos^2x + Cotx ÷ Cos^2x – Cotx = Cos^2x (tanx) + 1 ÷ Cos^2x (tanx) -1
  30. D

    Trig. identities method problem

    Question I've been struggling with the followings equations (I know that can be solved by Trig. identities method) and I tried almost everything but I can't get them right. the equations are the following: -Tab*cos(alpha)+Tbc*cos(beta) = 0 (eq.1) Tab*sin(alpha)+Tbc*sin(beta)=15 We know the...
  31. K

    How can I prove the trig identity sin2x = 2tanx/(tan^2x+1)?

    the follwing trig identity is used alot...but i am unable to proove it because i don't know wat to start with in solving it... sin2x=2tanx/(tan^2x+1) it invlves the double angle formulae i know that obviously, i tried substituting sin and cos into the RHS of equation and get my answer...
  32. K

    How Do You Prove Trigonometric Identities Involving Double Angles and Tangents?

    Hi, in this question i am nt sure the best way to tackle it! it follows proove the following 2sinxcosx=sqrt(3)-ssqrt(3)sin^2x for 0<=x<=360 i tried using the doble angle formulae on the right, putting all on one side therefore =0 (anticipating a quadratic equation) having...
  33. K

    Trigonometric Identities- simplify sin^4x - cos^4x

    hey just wonderin if any1 could give me a hint as to the best method to prove the following trigonometric indentity: sin^4x-cos^4x = 1 - 2cos^2x i tried the side more complicated first...but can't seem to hav any luck...other then maing it more complicated! umm the x's are meant to be...
  34. P

    Trigonometric Identities for Solving for Exact Values

    hey i have a problem which I am puzzled over. i I am given that: \sin A = \frac{3}{5} and i am asked to find exact values for: \sin 2A \cos 2A \tan 2A where 90^0 \leq A \leq 180^0 (the power to zero is the degree sign) i have gone about solving this by the use of a pythagorien (?) triple...
  35. P

    How can I prove the trigonometry identity \sin^4 - \cos^4 = 1 - 2\cos^2?

    i need to prove the following identity \sin^4 - \cos^4 = 1 - 2\cos^2 i have tried approaching this identity by solving the RHS (right hand side) of the equation but this lead no where. however i am unsure on how to maniplulate the LHS of this equation because of the power of 4. would...
  36. MathematicalPhysicist

    Proving Identities for 0<x<1: Integrals and Substitution Techniques

    i need to prove the next identities for 0<x<1: ∞ ∫t^(x-1)/(1+t)dt=π/sin(πx) 0 1 ∫t^(x-1)(1-t)^(-x)dt=π/sin(πx) 0 for the second one, my text gives me a hint to substitute t=u/(u+1), but i didnt succeed in getting the rhs. i tried the defintion of B(x,1-x)=Gamma(x)Gamma(1-x) but i...
  37. T

    This is a difficult problem- Identities

    Prove this identity: sin (2 X) ----------------- = 2 sin (X) - 2 sin^2 (X) sec (X) + tan (X) How would you do it? It was suggested in another thread that this can't be proved or that there is an error in the problem...but I think it is a hard problem to figure out. Anyeays, the...
  38. T

    Trig Identities Help Arrrggghhh

    Trig Identities Help...Arrrggghhh! :) I typed all of this out but the system then said I was not logged in and I lost it all...don't have time to retype everything. note: the ^ symbol is like "squared" for example, if I have 4^2 , that would be "four squared" or 4 times 4 = 16...
  39. X

    I proving two Trig identities

    1. Cos x (sec x + cos x csc^2 x) = csc^2 x I got as far as this... 1 + cos^2 + cos/sin^2 = csc^2 2. tan x(sin x + cot x cos x) = sec x
  40. W

    Proving Series Identities for -1<p<1

    The problem states: For -1<p<1 prove that, a) \sum p^n \cos nx = (1 - p\cos(x))/(1-2p\cos(x) + p^2) b) \sum p^n \sin nx = (1 - p\sin(x))/(1-2p\cos(x) + p^2) What I have been doing is searching for some type of expanding series for P^n\sin nx, however, I am pretty stumped
  41. K

    How Can I Simplify Trigonometric Identities for Tomorrow's Quiz?

    i had a test and i got a 55 can someone show me how to do these with the steps if possibleverify each of the folloring trigonomic identities 1) 2sin^2x - 1/sinx-cosx = sinx+cosx* did my steps wrong 2) cot^2x-cos^2x = cos^2xcot^2x didnt get an answer <no clue how to do simplify 1)...
  42. B

    Finding Exact Value of Cos A: Solutions Requested

    i and the rest of my class are finding it impossible to find the answer to this part of the question: find the exact value of cos A from secA-cosA=1/2 thanks in advance
  43. H

    Derive most trigonometric identities from the addition formulas

    In the same way that it is possible to derive most trigonometric identities from the addition formulas, what is the way that the difference of sines and cosines formulas were derived, such as \sin{a}-\sin{b}=2\cos{\frac{a+b}{2}}\sin{\frac{a-b}{2}} thanks, I am trying to avoid as much...
  44. JasonJo

    Calculating Lengths & Proving Identities: A Math Challenge

    1. calculate the length of the following paths: f(t) = (7, t, t^2) over 1<t<3 the way i was taught in class to calculate the length of a curve is to integrate the magnitude of the velocity, but i can't seem to naturally integrate the magnitude of (0, 1, 2t) similarly for: f(t) =...
  45. N

    Proving Identities with 0 < a in R

    How do you prove these? Let 0 < a, an element of R, and x, y an element of R. Then: (a^x)(a^y) = (a^(x+y)) a^(-x) = 1/(a^x) Thanks.
  46. G

    Using the identities to find the vales of each expression

    Ive been given very little notes from my teahcer, and can't do these. looked online, but its was no use. 1. Using the identities to find the vales of each expression (no calc.) (i) sin t = 15/17 , cos t = 8/17 find remaining trig functions (ii) sec^2 Pie/12 - tan^2 Pie/12 2. Find exact...
  47. G

    Using the identities to find the values of each expression

    Ive been given very little notes from my teahcer, and can't do these. looked online, but its was no use. 1. Using the identities to find the vales of each expression (no calc.) (i) sin t = 15/17 , cos t = 8/17 find remaining trig functions (ii) sec^2 Pie/12 - tan^2 Pie/12 2. Find exact...
  48. S

    Proving Identities and Double angles problems

    I've been working at proving these identites and I just can't seem to figure them out, some of them just come to me others I work on them for 10 mintues or more and just get more and more bogged down.:frown: 1) csc2x + cot2x = cotx so far i have 1/sin2x + cos2x/sin2x = cosx/sinx...
  49. C

    Solving Trig Identities: Tips for Getting Unstuck

    I can't get anywhere with these three identities. Any tips? \frac{(\sec \theta - \tan \theta)^2 + 1}{\csc \theta(\sec \theta - \tan \theta)} = 2 \tan \theta \frac{\sin^3 \theta + \cos^3 \theta}{\sin \theta + \cos \theta} = 1 - \sin \theta\cos \theta (2a\sin \theta\cos \theta)^2 +...
  50. M

    Solve Binomial Identities to Approximate Fresnel Zone Radius

    I was going the derivations for Fresnel zone radius approximation, and there was a jump in the math which I don't fully understand. If someone could take a look at this and help me figure. I was hinted that it had to do with the binomial theorem, but I have no idea >.< Seems like LaTeX isn't...
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