Trigonometry Examples

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

Step 1

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

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

Step 2

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

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

Step 3

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

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

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

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

Step 5

Separate fractions.

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

Step 6

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

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

Step 7

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

$\sin (x) \tan (x)$