Question

Prove that
sec^2A-cot^2 (90° - A)
= cos^2 (90° - A) + cos^2 A

Answer 1

hope this will help you

Answer 2

Hey !

LHS= sec²A-cot²(90-A)

= sec²A-tan²A [cot(90-A)=tanA ; 1+tan²A=sec²A]

= 1

RHS=cos²(90-A)+cos²A

=sin²A+cos²A

=1. [cos(90-A)=sinA ;sin²A+cos²A=1]

LHS=RHS

HENCE, Proved.