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. B

    Solve 3sin(x+10)=4cos(x-10) - Help!

    Solve for x 3sin(x+10)=4cos(x-10) I tried changinf everything into tan nothing out. I tried expaning the brackets and collecting like terms, that didnt work out either. Please help.
  2. B

    Trigonometric Identities: Simplifying and Proving

    I have been trying to solve this question for some time but I just cannot find the right solution: Simplify: 4cosec^2X + (4cosec^2X)(cot^2X)
  3. C

    What is the purpose of trigonometric identities

    As I rack my brains to solve(or atleast pretending) to prove Trig identites. What is it application in real life? :cry:
  4. C

    Differentiating Trig Identities: Example

    How can I use trig identities to let me differentiate \sin \left ( x + \frac{\pi}{2} \right) and 3 \sin x - 2 \cos x?
  5. C

    (e^ix)^n=(e^ixn) & Trig identities

    ok...this was meant to be a fun problem but looks like I don't deserve to have fun! How am I meant to derive trig identities like sin(x)cos^3(x) from some complex **** like \left( {e}^{{\it ix}} \right) ^{n}={e}^{{\it ixn}}! I just don't get the idea! :cry:
  6. S

    Understanding the Identities Theorem: Can You Solve this Problem?

    I need help on the following problem. (attached) Thanks
  7. M

    Use identities to Prove linearly idenpendent

    determine following setd of vectors in F(-infinitity, infinitiy) are linearly independent (using appropriate identities) 0, [cos (pi*x)]^3 , [sin 3*pi*x]^5 pls help !
  8. I

    Verifying Trig Identities help

    cos x - cos y sin x - sin y sin x + sin y + cos x + cos y = 0 or to see better i guess... (cos x - cos y)/(sin x + sin y) + (sin x - siny)/(cos x + cos y) = 0 can you guys help me? I'm really stuck on this!
  9. D

    Is there an easier approach for solving trigonometric identities?

    I'm having problems with it at school lately, I am not going to layout every single problem and ask for help. I am just wondering if there is a better approach to it rather than trying to solve one side in order to get it to equal the other side. For example, sin^2 x + cos^2 x = -cos^2 x - sin^2...
  10. N

    Proving an Equilateral Triangle: Trig Identities Explained

    Trig identities please help In triangle ABC if sin (A/2) sin (B/2) sin (C/2) = 1/8 prove that the triangle is equilateral please show steps
  11. C

    How Do I Solve Complex Trigonometric Identities?

    I can, for the mort part, understand how to derive and "proof" most of my Identity work, but some of the more complex (in my feeble opinion) problems give me quite a bit of trouble. Can anyone explain these? "Use the fundamental identities to simplify to sines and cosines: tan(^2)x -...
  12. T

    Trignometric identities question

    Hi, the question is 2sin^2 + sinX -1 = 0 I think the next step is then 2(1-cos^2)+cos^2=0 Did I do something wrong because I cannot seem to continue the question?
  13. F

    How can algebra and calculus be used to derive the identity for sin(a+b)?

    How do you find the identity for sin(a+b) using algebra or calculus? I already know how to do it with geometry and by using imaginary numbers.
  14. M

    Trignometric Identities Problem

    A little confused on how to begin the problem _1__ - tanx sinx = cosx cosx I know you change tanx to sinx/cosx but I can't seem to finish the problem, not sure if it is arithmatic errors or what?
  15. R

    Proof of cos(A+B) and sin(A+B) Identities

    How can you prove: cos(A+B)=cosAcosB-sinAsinB and similarly sin(A+B)=sinAcosB+cosAsinB If the proofs arent very complicated, I would appreciate you giving me hints first so maybe i can work them out on my own. Btw i am looking for an algebraic proof, not one with graphs & triangles.
  16. quasar987

    Unravelling the Mystery of logn Identities

    I don't get where these two identities come from: (logn)^{logn} = n^{log(logn)} and (logn)^{log(logn)} = e^{(log(logn))^2}
  17. X

    Trig Identities : Help 3 Questions.

    I can't get these 3 questions, can someone help me? 1. cotB [ (tanA + TanB) / (cotA+cotB) ] = tan A 2. (sin^2A + 2cosA - 1) / (2 + cosA - cos^2A) = 1 / (1+ secA) 3. cos^3A + sin^3A = (cosA+SinA)(1-SinAcosA) please help out on these, thanks in advance. U can write the / sign as...
  18. Loren Booda

    What makes your, of all identities, unique to yourself?

    Do self-awareness, social relativity, predestination, adaptation, deity or other circumstances determine who we really seem?
  19. S

    How do I prove the identity sin(4x) = 4sin(x)cos^3(x)-4sin^3(x)cos(x)?

    Hi all, I have a question proving an identity: sin(4x) = 4sin(x)cos^3(x)-4sin^3(x)cos(x) I can't seem to figure it out. I know I should be using the known identities: sin(2x) = 2sin(x)cos(x) and probably: cos(2x) = 1-2sin^2(x) but I'm stuck. Please help! Thanks!
  20. J

    Can You Solve These Trigonometric Identity Problems?

    Trig Identities question for test tomorrow Help! Need some help with these two problems: Thanks in advance if you could answer them: sin (X) / Cos (x) - 1 = show work Sec ^2/ cot (x) - Tan ^3x = Tan X show work to prove last one Sec x - Cos x/tanx = sinx show work to prove
  21. N

    How Do You Calculate tan2B if sinB = -5/13?

    Hi, today I was writing my Identities final test and got stuck on one question which I couldn't solve. The question was: If sinB=-\frac{5}{13} find the exact value of tan2B. I've got this far, correct me if I went wrong anywhere: tan2B=\frac{sin2B}{cos2B}=\frac{2sinBcosB}{2cos^2B-1}...
  22. M

    Tricky Tricky little Identities

    My friend sent me some Trigonometric proving identity questions to practise and i am usually good at them but i haven't done them for a while so i have gotten a bit rusty plus these ones to me are very difficult so i would like some assistance. Prove 1/1+sin + 1/1-sinx = 2secsquaredx. ok so...
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