Question

solve sin theta /1+cos theta +1-cos theta /sin theta =2 cosec thetaa

Answer 1

Step-by-step explanation:

solve it simply as isolve

Answer 2

Step-by-step explanation:

we use followin formula from sub multiple angles.

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

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

substitute in lhs

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