Question

If cot theta= 7/8, evaluate
1) ( 1+sin theta) ( 1-sin theta)/(1+cos theta)(1-cos theta )
2) cot 2 theta

Answer 1

$\cot( \alpha ) = \frac{7}{8}$
Implies that
$\tan( \alpha ) = \frac{8}{7} \\ \cos {}^{2} ( \alpha ) = (\frac{7}{ \sqrt{113} } ) {}^{2} = \frac{49}{113} \\ \sin( \alpha ) = \frac{64}{113}$
$\cot(2 \alpha ) = \frac{ \cot {}^{2} ( \alpha ) - 1}{2 \cot( \alpha ) }$