Simplify (sin(x)^2)/(cos(x)^2)+tan(x)cot(x)

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

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

Reorder $\tan (x)$ and $\cot (x)$ .

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

Rewrite $\tan (x) \cot (x)$ in terms of sines and cosines.

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

Cancel the common factors.

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

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

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

Apply pythagorean identity.

$\sec^{2} (x)$