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

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

Simplify each term.

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

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

Multiply $\frac{\cos (x)}{\sin (x)} \cos (x)$ .

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

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

Raise $\cos (x)$ to the power of $1$ .

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

Raise $\cos (x)$ to the power of $1$ .

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

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Add $1$ and $1$ .

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

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

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

Cancel the common factor of $\sin (x)$ .

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Simplify each term.

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

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

Separate fractions.

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

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

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

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

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