Trigonometry Examples

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

Step 1

Multiply by $1$ .

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

Step 2

Simplify with factoring out.

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Step 2.1

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

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

Step 2.2

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

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

Step 2.3

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

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

Step 3

Apply pythagorean identity.

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

Step 4

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

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Step 4.1

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

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Step 4.1.1

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

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

Step 4.1.2

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

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

Step 4.2

Add $1$ and $2$ .

$\cos^{3} (x)$