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

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

Step 1

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

Reorder $\sin (x)$ and $\csc (x)$ .

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

Rewrite $\sin (x) \csc (x)$ in terms of sines and cosines.

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

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.

$\sec^{2} (x)$