Question

show that cosec^2 theta- tan^2 (90-theta)= sin^2 + sin^2(90- theta)

Answer 1

L.h.s=cosec ^2x-cot^2x=1
R.h.s=sin^2x+cos^2x=1
So ,lhs= rhs

Answer 2

Cosec²∅ - tan²(90-∅) = LHS 

1/sin²∅ - cot²∅

1/sin²∅ - cos²∅/sin²∅

1-cos²∅/sin²∅

sin²∅ / sin²∅

1 

RHS = sin²∅ + sin²(90-∅) 

sin²∅ + cos²∅

1 

hence LHS = RHS