Simplify (1/(csc(x)))(tan(x)+cot(x))

$(\frac{1}{\csc (x)}) (\tan (x) + \cot (x))$

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

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

Multiply by the reciprocal of the fraction to divide by $\frac{1}{\sin (x)}$ .

$1 \sin (x) (\tan (x) + \cot (x))$

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

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

Apply the distributive property.

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

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

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

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

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

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

Cancel the common factors.

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