Question

1+tan^2(theta)/1+cot^(theta)=[1-tan(theta)]^2/[1-cot(theta)]^2

Answer 1

LS:

(1+tan^2)/(1+cot^2) * tan^2/tan^2
= tan^2(1+tan^2)/(tan^2+1)
= tan^2

RS:
(1-tan)^2/(1-cot)^2
= [(1-tan)/(1-cot)]^2
= [(1-tan)/(1-cot) * tan/tan]^2
= [tan(1-tan) / (tan-1)]^2
= [-tan]^2
= tan^2

LS = RS