Question

prove that tangent theta by 2 is equal to 1 minus cos theta by sin theta​

Answer 1

we need to prove

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

we know ,

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

also,

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

LHS=

tan alpha /2