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.

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- Mar 31st 2010, 07:54 PMBikkstahTrigonometric identity help
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. - Mar 31st 2010, 07:58 PMProve It
$\displaystyle (\csc{\theta} - \sin{\theta})^2 = \csc^2{\theta} - 2\csc{\theta}\sin{\theta} + \sin^2{\theta}$

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

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

$\displaystyle = \cot^2{\theta} - \cos^2{\theta}$. - Apr 1st 2010, 12:57 PMBikkstah
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.

- Apr 1st 2010, 01:03 PMe^(i*pi)
- Apr 1st 2010, 02:35 PMBikkstah
Thank you both so much!