Question

Prove that :-
(cos a - sin a + 1)/(cos a + sin a - 1) = (cosec a + cot a)

Answer 1

Answer:

( cos a + sin a - 1 ) ( cosec a + cot a )

= ( sin a + cos a - 1 ) ( 1 / sin a  + cos a / sin a )

= ( sin a + cos a - 1 ) ( 1 + cos a ) / sin a

= [ sin a ( 1 + cos a )  +  ( cos a - 1 ) ( 1 + cos a ) ] / sin a

= [ sin a ( 1 + cos a )  +  cos² a - 1 ] / sin a

= [ sin a ( 1 + cos a ) - sin² a ] / sin a

= 1 + cos a - sin a

=> ( cos a - sin a + 1 ) / ( cos a + sin a - 1 ) = ( cosec a + cot a )