Trigonometry Examples

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

Step 1

Multiply by $1$ .

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

Step 2

Simplify with factoring out.

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

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

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

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

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

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

Step 3

Apply pythagorean identity.

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

Step 4

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

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

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

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

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

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

Add $1$ and $2$ .

$\sin^{3} (x)$