Question

Prove that sec²θ + cosec²θ = sec²θ . cosec²θ

Answer 1

L.H.S. = sec² θ + cosec² θ = \(\frac{1}{cos^2\,\theta}+\frac{1}{sin^2\,\theta}\)

= \(\frac{sin^2\,\theta+cos^2\,\theta}{cos^2\,\theta.sin^2\,\theta}=\frac{1}{cos^2\,\theta.sin^2\,\theta}\)           (∵ sin² θ + cos² θ = 1)

= \(\frac{1}{cos^2\,\theta}\frac{1}{sin^2\,\theta}\) = sec² θ × cosec² θ