Expert: Paul Klarreich - 2/25/2009

Question
I got the teacher that doesn't teach he expects us to look a the problem and know exactly how to do it. I know this is tons of questions but I was hoping you could show me so i could be ready for my test. these are the ones im not sure about:


1.cos3x = 4cos^3x - 3cosx

2.cos5xcos3x + sin5xsin3x/sin3x-sinx = cscx/2

3.cosx/1-tanx = sinx/1-cotx = cosx + sinx

4.cosx + cos4x + cos7x/sinx +sin4x +sin7x = cot4x

5.cos^4x+ 1 - sin^4x= 2cos^2x

6.1 - sinxcosxtanx = cos^2x

7.tan1/2x = cscx - cotx

8. cscx/1 + cscx  -  cscx/1 - cscx = 2sec^2x




Thank you so much. This will help me greatly!

Answer
Questioner:  Lauren
Private: no
Subject:   
 
Question:  
I got the teacher that doesn't teach he expects us to look a the problem and know exactly how to do it. I know this is tons of questions but I was hoping you could show me so i could be ready for my test. these are the ones im not sure about:

1. cos3x = 4cos^3x - 3cosx

2. cos5xcos3x + sin5xsin3x/sin3x-sinx = cscx/2

3. cosx/1-tanx = sinx/1-cotx = cosx + sinx

4. cosx + cos4x + cos7x/sinx +sin4x +sin7x = cot4x

5. cos^4x+ 1 - sin^4x= 2cos^2x

6. 1 - sinxcosxtanx = cos^2x

7. tan1/2x = cscx - cotx

8. cscx/1 + cscx  -  cscx/1 - cscx = 2sec^2x

.........................
here is what you do:

When you see  sin or cos(2x) use one of the standard identities that you have memorized (I hope).

When you see  sin or cos(3x), write sinorcos(2x + x), then use one of the standard identities that you have memorized (I hope).

When you see tan or cot() use a quotient identity.

When you see sec or csc() use a reciprocal identity.

[CHEAT]  after all that, write C for cos x,  S for sin x, then do a lot of algebra.  When you see  sin^2 + cos^2, remember that is 1.

When you see something like  sin A cos B + cos A sin B, or anything else that looks like the right side of a standard identity, use the left side.

Now go to it, and send me what you have.  Then I'll try to help you.