identities Definition and 416 Threads

I have another answer to this but I believe this one is correct. I need someone else to check it out since I have been looking at it too long. Is the bottom equality correct? \begin{alignat*}{3} \frac{\partial^2}{\partial t^2}x_1 + x_1 & = & F\cos t - 2[-A'\sin t + B'\cos t] - c[-A\sin t +...

Sorry for the format, I'm on my phone. Lets say the matrix is | 1 1 1 | | a b c | | a^2 b^2 c^| Or {{1,1,1} , {a, b,c} , {a^2, b^2,c^2}} Show that it equals to (b-c)(c-a)(a-b) I did the determinant and my answer was (bc^2) - (ba^2) - (ac^2) + (ab^2) + (ca^2) - (cb^2)...

Apparently our professor expects us to know these half-angle identities (http://www.purplemath.com/modules/idents.htm) Without going through them in class or us learning them in high school.. Can somebody explain how these were derived? Does the derivation come from the angle-sum and...

∫(cot^4 x) (csc^4 x) dx Wolfram wants to use the reduction formula, but I'm meant to do this just using identities and u substitution. I was thinking something along the lines of: =∫cot^4 x (cot^2 x + 1)^2 dx =∫cot^8 x + 2cot^6 x + cot^4 x dx but I don't know where to go from there.

Homework Statement I need to prove the identity: (a×b)\cdot(c×d)= (a\cdotc)(b\cdotd)-(a\cdotd)(b\cdotc) using the properties of the vector and triple products: Homework Equations a×(b×c)=b(a\cdotc)-c(a\cdotb) a\cdot(b×c)=c\cdot(a×b)=b\cdot(c×a) The Attempt at a Solution I...

Does anyone know of websites where I can find many problems on the topic in the title line (my textbook has far too few)? Thanks!

1.) ∫[(7 sin (x))/[1+cos^2(x)]] * dx 2.) I'm looking at the trig identity sin^2 x+cos^2 x=1, and am wondering if I could use that in solving the problem. Or should I use u=sin x, then du= cos x, then plug those in? 3.) so I thought maybe it would be easier to separate the two...

Prove the identities $$ \frac{\sin\left(\frac{n + 1}{2}\theta\right)}{\sin\frac{\theta}{2}}\cos\frac{n}{2}\theta = \frac{1}{2} + \frac{\sin\left(n + \frac{1}{2}\right)\theta}{2\sin\frac{\theta}{2}} $$ By using the identity $\sin\alpha + beta$, I was able to obtain the $1/2$ but now I am not to...

Is this identity possible? cot 2x = \frac{cos3x + cosx}{sin 3x + sinx} Thanks!

Homework Statement Verify that \frac{cosθ}{1-tanθ} + \frac{sinθ}{1-cotθ} = sinθ + cosθ is an identity.Homework Equations - Reciprocal Trigonometric Identities - Pythagorean Trig IdentitiesThe Attempt at a Solution Every time I try to manipulate the LHS of the equation I always get -1 and as far...

Homework Statement Prove that sin6 + cos6 = 1 - 3sin2cos2 Homework Equations (1) The Attempt at a Solution I tried to convert those all in terms of sine and cosine only but it didn't work.

Homework Statement The two vectors a and b lie in the xy plane and make angles α and β with the x axis. a)By evaluating a • b in two ways (Namely a •b = abcos(θ) and a • b = a1b1+a2b2) prove the well-known trig identity cos(α-β)=cos(α)cos(β)+sin(α)sin(β) b)By similarly evaluating...

Homework Statement Prove that: (1-tanθ)/(1+tanθ)=(cotθ-1)/(cotθ+1) Homework Equations Trig Identities: tanθ= sinθ/cosθ cotθ= cosθ/sinθ 1+tanθ=secθ 1+cotθ=cosecθ The Attempt at a Solution These sorts of equations are coming up a lot and I am having trouble understanding...

Hello, Say I'm working with ∫ sqrt(1-cos(t)) dt I end up with a substitution of u = 1-cos(t) and dt = du/sin(t) sub back in: ∫ sqrt(u) / sin(t) du Still got a t in there ... hrrmmm So I go to wolfram alpha for some inspiration and 'show steps'...

Homework Statement Simplify the following: sin(b)/cos(b) + cos(b)/sin(b) Homework Equations Trigonometric identities The Attempt at a Solution Ok so i have no clue how to do this,I keep trying but can't seem to get the right answer, I have tried to do this: sin(b)/cos(b) +...

Hi, I am working on proofs of the difference identities for sine, cosine, and tangent. I am hoping to solve these using a specific diagram (attached). I was wondering if you could help me with the difference of cosines. Is it possible to derive it using the attached diagram? If so, how...

Homework Statement I need to show that ##\displaystyle\int_\Omega (\nabla G)w dxdy=-\int_\Omega (\nabla w) G dxdy+\int_\Gamma \hat{n} w G ds## given ##\displaystyle \int_\Omega \nabla F dxdy=\oint_\Gamma \hat{n} F ds## where ##\Omega## and ##\Gamma## are the domain and boundary respectively...

Homework Statement This isn't really a problem that was assigned to me, (I'm studying independently) I just have a question about the general concept behind some identities. Homework Equations sin(a+b) = sin(a)*cos(b) + cos(a)*sin(b) sin(theta) = sin(180-theta) The...

Fact: The ring of integers Z is totally ordered: for any distinct elements a and b in Z, either a>b or a<b. Fact: The ring of integers is discrete, in the sense that for any element a in Z, there exists an element b in Z such that there is no element c in Z with a<c<b, and the same argument...

I know you can derive the double angle formulas for sin(2a) and cos(2a) from Euler's identity, but is there any way to derive the tan(2a) in a similar manner from an easier formula? What about the addition/subtraction formulas (i.e. sin(a+b), etc.)

Is it possible to prove identities involving arctan by complex exponentiation? I had in mind something like the following for the arctan angle addition formula, but I feel there is something not quite right in the argument. $$\arctan{(a)}+\arctan{(b)}=...

Homework Statement Find the exact value of: sin (-5∏/12) 2. The attempt at a solution sin (-45° + -30°) = sin -45° cos -30° + cos -45° sin -30° = (sqrt (2) / 2 )(sqrt (3) / 2 ) + (sqrt (2) / 2)(1 / 2) = (sqrt (6) + sqrt (2)) / 4 However, the book has (-sqrt (6) -...

Hello all, I was wondering if someone has ever found a purely algebraic proof for the addition/subtraction theorems of trigonometry, mainly sin(a+b)=sin(a)cos(b)+sin(b)cos(a). Given a right triangle: Let x be one of the perpendicular legs and let the other leg be composed of two parts, y1...

Homework Statement Suppose f is a continously differentiable real valued function on R^3 and F is a continously differentiable vector field Prove 1)##\oint (f \nabla g +g\nabla f) \cdot dr=0## 2) ##\oint(f \nabla f)\cdot dr=0##Homework Equations ##\nabla f = f_z i+ f_y j+f_z k## Real valued...

Are there any useful identities for simplifying an expression of the form: $$((\ldots((x_{1} *_{1} x_{2}) *_{2} x_{3}) \ldots) *_{n - 1} x_{n})$$ Where each $$*_{i}$$ is one of $$\cap, \cup$$ and $$x_1 \ldots x_n$$ are sets? I believe I found two; though I haven't proved them, I think they...

Homework Statement Use fundamental identities to simplify the expression: (sinx)^2 - (cosx)^2 ____________________ (sinx)^2 - (sinx cosx)*note: it's a numerator and denominator. The underscore line is the fraction line. *note: The answer in the back of the book is "1 + cotx" but I would...

Is 2a/sin 2x equivalent to a cot x?

Hello! I've been tackling the question 'Express sin3x+sinx as a product and hence solve 1/2(sin3x+sinx)=sin2x ; x∈R' but I'm stumped - I'm not sure whether I've even approached it correctly. This is what I did: sin(3x+x)=sin3x.cosx+sinx.cos3x inserting this into the second equation...

Homework Statement Show the remainder when 43^43 is divided by 17. Homework Equations $$43 = 16 \times 2 + 11$$ $$a^{p-1}\equiv1\ (mod\ p)$$ The Attempt at a Solution I believe I can state at the outset that as: $$43\equiv9\ (mod\ 17)$$ Then $$43^{43}\equiv9^{43}\ (mod\ 17)$$ and that I...

If X and Y are binomial random variables with respective parameters (n,p) and (n,1-p), verify and explain the following identities: a.) P{X<=i}= P{Y>=n-i}; b.) P{X=k}= P{Y=n-k} Relevant Equations: P{X=i}=nCi *p^(i) *(1-p)^(n-i), where nCi is the combination of "i" picks given "n"...

Homework Statement Suppose c and (1 + ic)^{5} are real, (c ≠ 0) Show that either c = ± tan 36 or c = ± tan 72The Attempt at a Solution So I considered the polar form \left( {{\rm e}^{i\theta}} \right) ^{5} and that \theta=\arctan \left( c \right) , so c = tan θ Using binomial expansion, I...

Homework Statement The question is to find sin 2x, cos 2x, tan 2x from the given information: sin x = -\frac{3}{5}, x in Quadrant III Homework Equations Half Angle Identities cos2x = cos^{2}x - sin^{2}x sin2x = 2sinxcosx tan2x = \frac{2tanx}{2-tan^{2}x} The Attempt at a...

Homework Statement Use standard identities to express sin(x+pi/3) in terms of sin x and cos x Homework Equations sin(a+b)=sinAcosB+sinBcosA The Attempt at a Solution sin(x)cos(pi/3)+sin(pi/3)cos(x) 0.5sinx + 0.8660cosx I'm just not sure if i need to simplify it even further...

I am required to show that (i)in the upper limit of very high energies, the Born and eikonal identities are identical. (ii)that the eikonal amplitude satisfies the optical theorem. Regarding (i) I think it will involve changing from an exponential to a trig(Euler's theorem) but I could be...

Homework Statement \frac{∂x_{i}}{∂x_{j}} = δ_{ij} Homework Equations \vec{r} = x_{i}e_{i} The Attempt at a Solution \frac{∂x_{i}}{∂x_{j}} = 1 iff i=j δ_{ij} = 1 iff i=j therefore \frac{∂x_{i}}{∂x_{j}} = δ_{ij} Homework Statement r^{2} = x_{k}x_{k} Homework...

1. Sin^2(x) = 3 – x Answer: 2.97 Attempts: 1-cos^2(x) = 3 – x cos^2(x) - x + 2 = 0 Factored it and got x = pi = 3.14 It’s a multiple choice question, and other answers were 3.02,3.09 which are few decimal places off so the answer must not be pi since it's not even a choice. Is the...

hi.. i came through a problem in which the expression [1-(k(sin^2) θ)] has to be simplified.. can someone help me to solve it.??

Homework Statement Use Euler's identity to prove that cos(u)cos(v)=(1/2)[cos(u-v)+cos(u+v)] and sin(u)cos(v)=(1/2)[sin(u+v)+sin(u-v)] Homework Equations eui=cos(u) + isin(u) e-ui=cos(u)-isin(u) The Attempt at a Solution I was able to this with other trig identities with no...

Homework Statement ((cos x)/(1+sin x))+((1+sin x)/(cos x)) Homework EquationsThe Attempt at a Solution multiplied the left equation by (cos x)/(cos x) and the right fraction by (1+sin x)/(1+sin x) get ((cosx)^2 +(1+sinx)^2) / (1+sinx) (cos x) and I have no idea where to go from here

Homework Statement I have a problem. I need to prove that the divergence of Einstein tensor is 0 using the bianchi identities. I have looked to several sources and I have derived an answer, but I don't fully understand some steps. Homework Equations I have uploaded a document which shows a...

Homework Statement (3/5)cos2x + (3/5)sin2x The Attempt at a Solution I would think the answer would be 6/5, but it looks like the book is saying 3/5. I had a similar problem to this the other day and I tried finding it in my history but I couldn't.

Homework Statement Tan^3Theta Homework Equations Tan^2Theta=1-cos2Theta/1+cosTheta The Attempt at a Solution Attached

If an operation has two left identities, show that it has no right identity. _{} pf/ Let e_{1} and e_{2} be left identities such that e_{1}≠e_{2}. Assume there exist a right identity and call it r. Then we have that e_{1}x=x e_{2}x=x and xr=x. From here I want to...

Any/All help is appreciated :) Thanks! Homework Statement All that has to be done is proving that these two sides are equal. Basically, you just work through the problem until both sides are the same. (csc(x)-sec(x))/(csc(x)+sec(x)) = (tan(x)-1)/(tan(x)+1) Homework Equations...

Where would be the best place to find every trigonometric identity, from sin[2] + cos[2] = 1, to the matrix identities (and Euler's equation would be helpful, also) Also the location of mathematical analysis symbols would be helpful, also. Thank you very much in advance :)

Please, check my work. Homework Statement a) Show that sqrt{[1+tan^2x]/[1+cot^2x]}=tanx b) Show that [cosx+sinx]/[cosx-sinx]=1+[2tanx]/[1- tanx] c)Show that cotxcosx+tanxsinx=(cosecx+ secx)(1-sinxcosx) d) Show that cosec^2x-cosecx=cot^2x/[1+sinx] e) Show that sin^3x-cos^3x=...

My homework is to find the sin or cos value of angle that is not directly known on the unit circle. So of course we are given an equation which adds or subracts known values to get the desired one. The problem is that I don't think memorizing them is helping me learn. I want to know how the...

Alright, well I am having a difficult time getting these equations to equal out! I keep hitting trouble and have hit a road block. Here is the problem... csc(x)+cot(x) = cot(x)csc(x) tan(x)+sin(x) I am just going to work on the LEFT PART of the equation. 1 + cos(x) sin(x)...

Hi, I am given that, for π/2 < x < π, sin x = 2/√13 a) Find Cos x b) Find tan 2 x So, what I did was: I drew a triangle and found that the missing side was equal to 3. From then, I deduced that cos x was equal to 3/√13 The problem was however that the angle must lie between the...

Hello all, I'm wanting to learn how to derive all of the trig identities (well, not all, but the most common) rather than memorizing them. Perhaps someone here could provide me with a list of "essentials" that are the framework for deriving others. For example, I know there are a few that can...