Question

what is root of 1+cos theta/1-cos theta

Answer 1

$\sqrt{ \frac{1 + \cos( \alpha ) }{1 - \sin( \alpha ) } } \\ \sqrt{ \frac{2 { \cos( \frac{ \alpha }{2} ) }^{2} }{2 \sin( \frac{ \alpha }{2}) } } \\ \tan( \frac{ \alpha }{2} )$

$since \: we \: know \: that \: \\ 1 + \cos( \alpha ) = 2 { \cos( \frac{ \alpha }{2} ) }^{2} \\ 1 - \cos( \alpha ) = 2 { \sin( \frac{ \alpha }{2} ) }^{2}$

Answer 2

Step-by-step explanation:

using formula ,

$1+\cos(\alpha ) = 2\ \cos{}^{2} (\frac{ \alpha }{2} )$

$1-\cos(\alpha )=2\sin {}^{2} ( \frac{ \alpha }{2} )$

Now ,

we have to find the value of

$\sqrt{ \frac{1 + \cos( \alpha ) }{1 - \cos( \alpha ) } }$

$=> \: \sqrt{ \frac{2 \cos {}^{2} ( \frac{ \alpha }{2} ) }{2 \sin {}^{2} ( \frac{ \alpha }{2} ) } }$

$=> \: \cot( \frac{ \alpha }{2} )$