Trigonometric identity help

**Bikkstah** · March 31st 2010, 07:54 PM

Hi all,

I am stuck on proving these two problems:

(csc theta - sin theta)^2 = cot^2theta - cos^2theta

and

(1+cos2theta/cos^2theta)=2

I know I need to use double angle identities in the second one, but I have been stuck on how to get going.

**Prove It** · March 31st 2010, 07:58 PM

Originally Posted by Bikkstah

Hi all,

I am stuck on proving these two problems:

(csc theta - sin theta)^2 = cot^2theta - cos^2theta

and

(1+cos2theta/cos^2theta)=2

I know I need to use double angle identities in the second one, but I have been stuck on how to get going.

$(\csc{\theta} - \sin{\theta})^2 = \csc^2{\theta} - 2\csc{\theta}\sin{\theta} + \sin^2{\theta}$

$=\csc^2{\theta} - 2 + \sin^2{\theta}$

$= \csc^2{\theta} - 1 - (1 - \sin^2{\theta})$

$= \cot^2{\theta} - \cos^2{\theta}$ .

**Bikkstah** · April 1st 2010, 12:57 PM

Can anyone help with (1 + Cos2theta/cos^2theta)=2? I know it's true by setting theta equal to a real angle like 30 degrees, but I don't know how to prove it using just identities.