# identity

1. ### Prove Identity

I've tried starting from both sides, using sin and cos double angle formula, but I seem to be getting nowhere. Please could someone outline the steps.
2. ### Square Root of One - sin(theta) cos(theta): Identity?

In some recent work, I have manipulated an equation into the following form: y = \sqrt{(1 - (sin(\theta ) cos(\theta ))^{2})} Is there an identity to simplify this equation? Nothing is coming to mind. I suppose a temporary variable could be defined, say, B, such that (i) cos(B) =...
3. ### Trig Identity Help

Hi I have got a trig identity question which i am really struggling with, if anyone could help me. Prove the identity Cos3Θ = 4Cos^3Θ - 3CosΘ hint express 3CosΘ as Cos(2Θ + Θ) I have got as far as the hint and then i am stuck. Cos(2Θ + Θ) = 4Cos^3Θ - 3CosΘ Can anyone guide me in the...
4. ### Trigonometry Identity

1/(1+sec(s))+1/(1-Sec(s))=-2cot^2(s) I have been working on this for over an hour, I just cant find a way.
5. ### Set Identity help

can somebody explain what the name of this property is. i cant find it anywhere in my textbook. and why does it work? heres a bigger version of the image if u cant see. http://i.imgur.com/uM7lD5y.png
6. ### Trigonometric Identity

(SinB)/(1+cosB)+(1+cosB)/(SinB)= 2cscB So I get them to common denominators and add them, but I have a trouble factoring them, how would one approach this.
7. ### Vector Identity

Show that: a x ( b x c) + b x ( c x a) + c x (a x b ) =0 Can't quite figure this one out. I have got it to (axb)+(bxa)+(axc)+(cxa)+(axb)+(bxa).
8. ### Prove identity

I'm stuck on this problem... Can anyone point me in the right direction? I'm having trouble simplifying it. a = \displaystyle{\frac{sin^2(K \varphi) + sin \varphi \cdot sin(2K+1)\varphi }{sin \varphi}} b = \frac{sin^2(K +1) \varphi }{sin \varphi} Prove that a=b.
9. ### Trig Identity

2\sin(x)\cos(x) = \sin(2x) so \sin(x)\cos(x) = \dfrac{1}{2}\sin(2x) ??? 2\sin(30)\cos(30) = \sin(2(30)) \dfrac{\sqrt{3}}{2} = \dfrac{\sqrt{3}}{2} \cos(30)\sin(30) = \dfrac{1}{2}\sin((2)(30)) \dfrac{\sqrt{3}}{4} = \dfrac{\sqrt{3}}{4} ??
10. ### sin^4(Ө) = 3/8-3/8 cos(2Ө). Prove the trigonometric identity

So far I have gotten that i need to expand the equation so I separated the equation into (1- cos^2Ө)(1- cos^2Ө) = 1- 2cos^2Ө + (cos^2Ө)^2. I reduced it because sin^2Ө = 1 – cos^2Ө and after that I'm lost. I think I am supposed to use the power reducing formula but i dont know how to get it...
11. ### Trig identity?

T = THETA. I have worked out from an engineering problem that cos(T) = 5/6 (without using a calculator). but I have to find out what cos2(T) is for the following equation h= r(1-cos2(T)) r is the radius which is 48, I just don't understand how to get to cos2(T) from cos(T). Is it possibly to...
12. ### prove each identity

i'm stuck on this one sinx+sinxcot^2x=cscx LS sinx+sinxcos^2X/sin^2 i'm lost after this-- can you explain how you get to each of the next steps?
13. ### The equation sin(x)=√2/2 is an identity. True or false?

The equation sin(x)=√2/2 is an identity. True or false?
14. ### Double Angle Identity with tan()

Hello, I am trying to do this problem, but cannot figure out how to do this with tangent. Thanks in advance!
15. ### help solving trigonometric identity

\frac{1-tan^2x}{1-cot^2x} = 1-sec^2x Trying to solve left side. changing the cot^2x into \frac{1}{tan^2x} \frac{1-tan^2x}{1-\frac{1}{tan^2x}} simplifying I get: \frac{tan^2x(1-tanx)}{tanx-1} change tan^2x into sec^2x-1 \frac{(sec^2x-1)(1-tanx)}{tanx-1} I don't know what to do after...
16. ### Prove Hyperbolic Identity.

Hi everyone, Would any of you lovely people be able to help me with this question please. Prove the hyperbolic Identity sinh 2A = 2 sinh A cosh A, by replacing cosh and sihn by their representation using ex approach Thanks in advance Sam
17. ### Proving identity for sum of squares of first n natural numbers

Hi, Prove 1^2 + 2^2 + \cdots + n^2 = \frac{n^3}{3}+\frac{n^2}{2}+\frac{n}{6}, where n \ge 1. I don't understand the following proof. Mainly: Why start with the formula (k+1)^3? Why take k = 1,2,\cdots, n-1? Why only up to n-1 and not n? Does n-1 represent the previous term in the sequence or...
18. ### Help with explaining this trigonometric identity example?

In my homework, there is this rather difficult trig identity example. I understand it for the most part until it came to factoring. Here is what is shown: sinx + tanx = tanx (1 + cosx) Working from the LHS... sinx + tanx sinx + (sinx/cosx) + sinx/cosx sinxcosx+sinx/cosx --- Now here...
19. ### Euler's Identity problem

Euler's Identity problem (Solved) My problem goes as follows: Use Euler's Identity to find A and B so that (cos(x))^3 = A*cos(3x) + B*cos(x) Any help would be greatly appreciated!! I have no clue where to start.
20. ### Identity permutation has odd number of transpositions?

Suppose there is a group of permutation of a set with Now this group has identity permutation( ) and inverse permutation( ) namely: and But there is a theorem which says that: "No matter how is written as a product of transpositions, the number of transpositions is even." Now by...