Question

Prove the following.
sec²θ + cosec²θ = sec²θ × cosec²θ 

Answer 1

\[\sec^2 \theta + {cosec}^2 \theta\]
\[ = \frac{1}{\cos^2 \theta} + \frac{1}{\sin^2 \theta}\]
\[ = \frac{\sin^2 \theta + \cos^2 \theta}{\cos^2 \theta \sin^2 \theta}\]
\[ = \frac{1}{\cos^2 \theta \sin^2 \theta}\]
\[ = \frac{1}{\cos^2 \theta} \times \frac{1}{\sin^2 \theta}\]
\[ = \sec^2 \theta  \text{ cosec }^2 \theta\]