Question

Simplify it -

$\frac{\cos 2x+2{\sin }^{2}x}{{\cos }^{2}x}$

Answer 1

Consider the following question.

$\frac{\cos 2x+2{\sin }^{2}x}{{\cos }^{2}x}$

$=\frac{{\cos }^{2}x-{\sin }^{2}x+2{\sin }^{2}x}{{\cos }^{2}x}$

$=\frac{{\sin }^{2}x+{\cos }^{2}x}{{\cos }^{2}x}$

$=\frac{1}{{\cos }^{2}x}$

$={\sec }^{2}x$

Hence, this is the required answer.