# How do you simplify (cos2x+sin^2x)/cos^2x?

$1$
Recall the identity $\cos 2 x = {\cos}^{2} x - {\sin}^{2} x$. Applying it, we get
$\frac{{\cos}^{2} x \cancel{- {\sin}^{2} x + {\sin}^{2} x}}{\cos} ^ 2 x = \frac{\cancel{{\cos}^{2} x}}{\cancel{{\cos}^{2} x}} = 1$