# Prove these identities.

• July 20th 2009, 09:28 PM
hellojellojw
Prove these identities.
cos(5w) + cos(w) cot(2w)
----------------- = ----------
cos(w) - cos(5w) tan(3w)

and

cos^2(1/2x) - sin^2 (1/2x) = cosx

Lol alright.

For the 1st one. I just used a sum product identity on the left side of the equation, but came up with just cot(2w) * cot(3w). Am I missing something?

and for the 2nd one, I don't know what identity to use lol
• July 20th 2009, 09:34 PM
Krizalid
Quote:

Originally Posted by hellojellojw

No.

I think you can change that sentence by rewritting it as "show hints please!" Or show what have you done.
• July 20th 2009, 09:40 PM
hellojellojw
Quote:

Originally Posted by Krizalid
No.

I think you can change that sentence by rewritting it as "show hints please!" Or show what have you done.

Okay, I understand.
• July 20th 2009, 09:58 PM
yeongil
Quote:

For the 1st one. I just used a sum product identity on the left side of the equation, but came up with just cot(2w) * cot(3w). Am I missing something?
You're very close.
$\cot 2w \cot 3w = \frac{\cot 2w}{\tan 3w}$. Remember that tangent and cotangent are reciprocals?

Quote:

and for the 2nd one, I don't know what identity to use lol
Try the cosine of a double angle formula.

01
• July 20th 2009, 10:35 PM
hellojellojw
Quote:

Originally Posted by yeongil
You're very close.
$\cot 2w \cot 3w = \frac{\cot 2w}{\tan 3w}$. Remember that tangent and cotangent are reciprocals?

Try the cosine of a double angle formula.

01

oh wow didn't notice that before. Thanks
For the cosine double angle formula, do I need to show steps? I mean it looks the same, its just theta divided by 2.
• July 20th 2009, 10:42 PM
VonNemo19
Quote:

Originally Posted by hellojellojw
oh wow didn't notice that before. Thanks
For the cosine double angle formula, do I need to show steps? I mean it looks the same, its just theta divided by 2.

When proving something, always show steps, or at least make note of them.