Question

Simplify $\frac{\cos 2x+2{\sin }^{2}x}{co{s}^{2}x}$

Answer 1

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

$=\frac{2{\cos }^{2}x-1+2{\sin }^{2}x}{{\cos }^{2}x}$

$=\frac{2({\cos }^{2}x+{\sin }^{2}x)-1}{{\cos }^{2}x}$

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

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

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

Hence, this is the answer.