Question

SinA/1+cosA=cosecA-cotA

Answer 1

TO PROVE :

$\frac{ \sin(a) }{1 + \cos(a) } = \csc(a) - \cot(a)$

PROOF =>

LHS =

$\frac{ \sin(a) }{1 + \cos(a) }$

Multiply , (1 - cos A) in numerator and denominator , we get ,

=> sin A ( 1 - cos A ) / ( 1 + cos A) ( 1 - cos A )

=> sin A ( 1 - cos A ) / sin² A

As , sin² A + cos² A = 1

=> 1-cos² A = sin² A

=> ( 1 + cos A) (1 - cos A) = sin² A

and ,

=> ( 1 - cos A ) / sin A

=> 1 / sin A - cos A / sin A

=> cosec A - cot A = RHS .....

PROVED!