Trigonometry Examples

$120 {\cos (x)}^{2^{1}} \cdot \sin^{4} (x) + 40 \cos^{6} (x)$

Step 1

Factor $40$ out of $120 {\cos (x)}^{2^{1}} \cdot \sin^{4} (x) + 40 \cos^{6} (x)$ .

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Step 1.1

Factor $40$ out of $120 {\cos (x)}^{2^{1}} \cdot \sin^{4} (x)$ .

$40 (3 {\cos (x)}^{2^{1}} \cdot \sin^{4} (x)) + 40 \cos^{6} (x)$

Step 1.2

Factor $40$ out of $40 \cos^{6} (x)$ .

$40 (3 {\cos (x)}^{2^{1}} \cdot \sin^{4} (x)) + 40 (\cos^{6} (x))$

Step 1.3

Factor $40$ out of $40 (3 {\cos (x)}^{2^{1}} \cdot \sin^{4} (x)) + 40 (\cos^{6} (x))$ .

$40 (3 {\cos (x)}^{2^{1}} \cdot \sin^{4} (x) + \cos^{6} (x))$

Step 2

Evaluate the exponent.

$40 (3 \cos^{2} (x) \sin^{4} (x) + \cos^{6} (x))$

Step 3

Factor.

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Step 3.1

Factor $\cos^{2} (x)$ out of $3 \cos^{2} (x) \sin^{4} (x) + \cos^{6} (x)$ .

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Step 3.1.1

Factor $\cos^{2} (x)$ out of $3 \cos^{2} (x) \sin^{4} (x)$ .

$40 (\cos^{2} (x) (3 \sin^{4} (x)) + \cos^{6} (x))$

Step 3.1.2

Factor $\cos^{2} (x)$ out of $\cos^{6} (x)$ .

$40 (\cos^{2} (x) (3 \sin^{4} (x)) + \cos^{2} (x) \cos^{4} (x))$

Step 3.1.3

Factor $\cos^{2} (x)$ out of $\cos^{2} (x) (3 \sin^{4} (x)) + \cos^{2} (x) \cos^{4} (x)$ .

$40 (\cos^{2} (x) (3 \sin^{4} (x) + \cos^{4} (x)))$

Step 3.2

Remove unnecessary parentheses.

$40 \cos^{2} (x) (3 \sin^{4} (x) + \cos^{4} (x))$