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.
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.
$\displaystyle (\csc{\theta} - \sin{\theta})^2 = \csc^2{\theta} - 2\csc{\theta}\sin{\theta} + \sin^2{\theta}$
$\displaystyle =\csc^2{\theta} - 2 + \sin^2{\theta}$
$\displaystyle = \csc^2{\theta} - 1 - (1 - \sin^2{\theta})$
$\displaystyle = \cot^2{\theta} - \cos^2{\theta}$.