# Question #24c10

Feb 9, 2017

Explained below

#### Explanation:

In the numerator on the left side add and subtract 1 as,

$1 + {\tan}^{2} \theta + {\cos}^{2} \theta - 1$

or, $1 + {\tan}^{2} \theta - \left(1 - {\cos}^{2} \theta\right)$

or, ${\sec}^{2} \theta - {\sin}^{2} \theta$

or, $\frac{1}{{\cos}^{2} \theta} - {\sin}^{2} \theta$. Now factorise it,

$\left(\frac{1}{\cos} \theta - \sin \theta\right) \left(\frac{1}{\cos} \theta + \sin \theta\right)$

The factor $\left(\frac{1}{\cos} \theta + \sin \theta\right)$ would get cancelled out with the denominator, leaving with the factor $\frac{1}{\cos} \theta - \sin \theta$= RHS