Trigonometry Examples

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

Step 1

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

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

Step 2

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

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

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Reduce the expression $\frac{\sin^{2} (x) \cos (x)}{\sin (x)}$ by cancelling the common factors.

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Step 3.1.1

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

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

Step 3.1.2

Multiply by $1$ .

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

Step 3.1.3

Cancel the common factor.

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

Step 3.1.4

Rewrite the expression.

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

Step 3.2

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

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

Step 4

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

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Step 4.1

Cancel the common factor.

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

Step 4.2

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

$\sin (x)$