Question

Prove that `(tan^2 θ)/(1 + tan^2 θ) + (cot^2 θ)/(1 + cot^2 θ) = 1`

Answer 1

L.H.S. = `(tan^2 θ)/(1 + tan^2 θ) + (cot^2 θ)/(1 + cot^2 θ)`

= `(tan^2 θ)/(sec^2 θ) + (cot^2 θ)/("cosec"^2 θ)`

= `((sin^2 θ)/(cos^2 θ))/(1/(cos^2 θ)) + ((cos^2 θ)/(sin^2 θ))/(1/(sin^2 θ))`

= sin²θ + cos²θ

= 1

= R.H.S.

Hence Proved.