Question

Prove that
sinA/1-cosA=cotA/2​

Answer 1

Explanation:

`( \sin(A) )/(1 - \cos(A) ) = \frac{ \sin(A)(1 + \cos(A) ) }{( {1}^(2) + { \cos }^(2)A) } \\ = (\sin(A) + \sin(A) \cos(A) )/(1 - \cos ^(2) (A) ) \\ = (\sin(A) + \sin(A) \cos(A) )/( \sin ^(2) (A) ) \\ = (1 + \cos(A) )/( \sin(A) ) \\ for \: half \: angles \\ = (1 + (2 \cos ^(2) ( (A)/(2) ) - 1))/(2 \sin( (A)/(2)) \cos( (A)/(2) ) ) \\ = \frac{ { \cos }^(2) (A)/(2) }{ \sin( (A)/(2) ) \cos( (A)/(2) ) } \\ = ( \cos( (A)/(2) ) )/( \sin( (A)/(2) ) ) \\ = \cot( (A)/(2) )`