# Question #b851d

Jan 25, 2017

Blank should be filled in by ${\cos}^{2} \theta$

#### Explanation:

If ${\cos}^{2} \theta$ is written in the blank then LHS becomes

$L H S = 1 - {\tan}^{2} \theta \times {\cos}^{2} \theta$

$= {\sec}^{2} \theta {\cos}^{2} \theta - {\sin}^{2} \frac{\theta}{\cos} ^ 2 \theta \times {\cos}^{2} \theta$

$= {\sec}^{2} \theta {\cos}^{2} \theta - {\sin}^{2} \theta = R H S$