Trigonometry Examples

$\frac{\sin^{4} (x)}{\tan^{2} (x)}$

Step 1

Simplify the denominator.

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Step 1.1

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

$\frac{\sin^{4} (x)}{{(\frac{\sin (x)}{\cos (x)})}^{2}}$

Step 1.2

Apply the product rule to $\frac{\sin (x)}{\cos (x)}$ .

$\frac{\sin^{4} (x)}{\frac{\sin^{2} (x)}{\cos^{2} (x)}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$\sin^{4} (x) \frac{\cos^{2} (x)}{\sin^{2} (x)}$

Step 3

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

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Step 3.1

Factor $\sin^{2} (x)$ out of $\sin^{4} (x)$ .

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

Step 3.2

Cancel the common factor.

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

Step 3.3

Rewrite the expression.

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