Question

(cosec a -sin a) (sec a-cosa) =1/tana+cota
Simplify lhs and rhs separately

Answer 1

Step-by-step explanation:

LHS: (coseca-sina)(seca-cosa)

= (1 / sina-sina)(1 / cosa-cosa)

= (1-sin^2a / sina)(1-cos^2a / cosa)

= (1-sin^2a)(1-cos^2a) / sina.cosa

= (cos^2a)(sin^2a) / sina.cosa

= sina.cosa

RHS: 1/tana+cota

= 1 / (sina/cosa)(cosa/sina)

= 1 / [ (sin^2a + cos^2a) / (sina.cosa) ]

= sina.cosa

Therefore, LHS=RHS