Simplify (sin(x)^2)/(cos(x)^2)+cos(x)sec(x)

$\frac{\sin^{2} (x)}{\cos^{2} (x)} + \cos (x) \sec (x)$

Step 1

Rewrite in terms of sines and cosines, then cancel the common factors.

Reorder $\cos (x)$ and $\sec (x)$ .

$\frac{\sin^{2} (x)}{\cos^{2} (x)} + \sec (x) \cos (x)$

Rewrite $\cos (x) \sec (x)$ in terms of sines and cosines.

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

Cancel the common factors.

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

Step 2

Convert from $\frac{\sin^{2} (x)}{\cos^{2} (x)}$ to $\tan^{2} (x)$ .

$\tan^{2} (x) + 1$

Step 3

Apply pythagorean identity.

$\sec^{2} (x)$