Precalculus Examples

$\tan^{2} (3 x)$

Step 1

Apply the tangent triple-angle identity.

${(\frac{3 \tan (x) - \tan^{3} (x)}{1 - 3 \tan^{2} (x)})}^{2}$

Step 2

Factor $\tan (x)$ out of $3 \tan (x) - \tan^{3} (x)$ .

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Step 2.1

Factor $\tan (x)$ out of $3 \tan (x)$ .

${(\frac{\tan (x) \cdot 3 - \tan^{3} (x)}{1 - 3 \tan^{2} (x)})}^{2}$

Step 2.2

Factor $\tan (x)$ out of $- \tan^{3} (x)$ .

${(\frac{\tan (x) \cdot 3 + \tan (x) (- \tan^{2} (x))}{1 - 3 \tan^{2} (x)})}^{2}$

Step 2.3

Factor $\tan (x)$ out of $\tan (x) \cdot 3 + \tan (x) (- \tan^{2} (x))$ .

${(\frac{\tan (x) (3 - \tan^{2} (x))}{1 - 3 \tan^{2} (x)})}^{2}$

Step 3

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 3.1

Apply the product rule to $\frac{\tan (x) (3 - \tan^{2} (x))}{1 - 3 \tan^{2} (x)}$ .

$\frac{{(\tan (x) (3 - \tan^{2} (x)))}^{2}}{{(1 - 3 \tan^{2} (x))}^{2}}$

Step 3.2

Apply the product rule to $\tan (x) (3 - \tan^{2} (x))$ .

$\frac{\tan^{2} (x) {(3 - \tan^{2} (x))}^{2}}{{(1 - 3 \tan^{2} (x))}^{2}}$