Question

Evaluate: $\left(1+{\tan }^2\theta \right){\cos }^2\theta .$

Answer 1

Given data: $\left(1+{\tan }^2\theta \right){\cos }^2\theta$

Evaluating the given expression:

$\begin{array}{rcl}\left(1+{\tan }^2\theta \right){\cos }^2\theta & =& se{c}^2\theta \times {\cos }^2\theta \left[\because 1+{\tan }^2\theta =se{c}^2\theta \right]\\ & =& \frac{1}{{\cos }^2\theta }\times {\cos }^2\theta \\ & =& 1\end{array}$

Hence, $\left(1+{\tan }^2\theta \right){\cos }^2\theta$ is equal to $1$.