Trigonometry Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

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

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

Step 1.3

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

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

Step 2

Rearrange terms.

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

Step 3

Apply pythagorean identity.

$2 \sin (x) \cos (x) \cdot 1$

Step 4

Apply the sine double-angle identity.

$\sin (2 x) \cdot 1$

Step 5

Multiply $\sin (2 x)$ by $1$ .

$\sin (2 x)$