Simplify sin(x)tan(x)cot(x)csc(x)

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

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

$\sin (x) \frac{\sin (x)}{\cos (x)} \cot (x) \csc (x)$

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

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

$\frac{\sin (x) \sin (x)}{\cos (x)} \cot (x) \csc (x)$

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

Combine.

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

Cancel the common factor of $\sin^{2} (x)$ and $\sin (x)$ .

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

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

Cancel the common factors.

Factor $\sin (x)$ out of $\cos (x) \sin (x)$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

Cancel the common factor.

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

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

$\sin (x) \csc (x)$

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

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

$\csc (x) \sin (x)$

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

$\frac{1}{\sin (x)} \sin (x)$

Cancel the common factors.

$1$