Precalculus Examples

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

Step 1

Simplify with factoring out.

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Step 1.1

Reorder $\sin (x) \cdot \cos^{2} (x)$ and $- \sin (x)$ .

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

Step 1.2

Factor $- \sin (x)$ out of $- \sin (x)$ .

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

Step 1.3

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

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

Step 1.4

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

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

Step 1.5

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

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

Step 2

Apply pythagorean identity.

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

Step 3

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

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Step 3.1

Move $\sin^{2} (x)$ .

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

Step 3.2

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

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Step 3.2.1

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

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

Step 3.2.2

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

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

Step 3.3

Add $2$ and $1$ .

$- \sin^{3} (x)$