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

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

Step 1

Simplify each term.

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

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

Combine $\frac{1}{\cos (x)}$ and $\sin^{2} (x)$ .

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

Step 2

Simplify each term.

Factor $\sin (x)$ out of $\sin^{2} (x)$ .

$\frac{\sin (x) \sin (x)}{\cos (x)} + \cos (x)$

Separate fractions.

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

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

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

Divide $\sin (x)$ by $1$ .

$\sin (x) \tan (x) + \cos (x)$