Question

Prove that (1+tan²A)/(1+cot²A) = (1-tanA)²/(1-cotA)²

Answer 1

LHS:
(1+tan²A)/(1+cot²A)
=(1+tan²A)/(1+1/tan²A)
=(1+tan²A)/[(1+tan²A)/tan²A]
=tan²A
RHS:
(1-tanA)²/(1-cotA)²
=(1-2tanA+tan²A)/(1-2cotA+cot²A)
=(1-2tanA+tan²A)/(1-2/tanA+1/tan²A)
=(1-2tanA+tan²A)/[(tan²A-2tanA+1)/tan²A]
=tan²A
∴, LHS=RHS(Proved)