Question

Prove that: tan² θ + cot² θ + 2 = sec² θ cosec² θ.

Answer 1

LHS = tan² θ + cot² θ + 2

= sec² θ – 1 + cosec² θ – 1 + 2

= sec² θ + cosec² θ – 2 + 2

= `1/(cos^2θ) + 1/(sin^2θ)`

= `(sin^2θ + cos^2θ)/(cos^2θsin^2θ)`

= `1/(cos^2θ sin^2θ)`

= sec² θ cosec² θ = RHS

Hence proved.