Question

Prove that sec 2 0 + cot 2 (90 -0) = 2cosec 2 (90 -0) -1

Answer 1

LHS
=sec²θ+cot²(90°-θ)
=sec²θ+tan²θ [∵, cot(90°-θ)=tanθ]
=sec²θ+(sec²θ-1) [∵, sec²θ-tan²θ=1]
=2sec²θ-1
RHS
=2cosec²(90°-θ)-1 [∵, cosec(90°-θ)=secθ]
=2sec²θ-1
∴, LHS=RHS (Proved)