Precalculus Examples

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

Step 1

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

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Step 1.1

Reorder $\cos (x)$ and $\tan (x)$ .

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

Step 1.2

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

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

Step 1.3

Cancel the common factors.

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

Step 2

Multiply by $1$ .

$\sin (x) \cdot 1 - \sin (x) \cos^{2} (x)$

Step 3

Simplify with factoring out.

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Step 3.1

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

$\sin (x) \cdot 1 + \sin (x) (- 1 \cos^{2} (x))$

Step 3.2

Factor $\sin (x)$ out of $\sin (x) \cdot 1 + \sin (x) (- 1 \cos^{2} (x))$ .

$\sin (x) \cdot (1 - 1 \cos^{2} (x))$

Step 3.3

Rewrite $- 1 \cos^{2} (x)$ as $- \cos^{2} (x)$ .

$\sin (x) \cdot (1 - \cos^{2} (x))$

Step 4

Apply pythagorean identity.

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

Step 5

Multiply $\sin (x)$ by $\sin^{2} (x)$ by adding the exponents.

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Step 5.1

Multiply $\sin (x)$ by $\sin^{2} (x)$ .

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Step 5.1.1

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

$\sin^{1} (x) \cdot \sin^{2} (x)$

Step 5.1.2

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

${\sin (x)}^{1 + 2}$

Step 5.2

Add $1$ and $2$ .

$\sin^{3} (x)$