Trigonometry Examples

$\sin (x) + 2 \sin (x) \cos (x)$

Step 1

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

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Step 1.1

Multiply by $1$ .

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

Step 1.2

Factor $\sin (x)$ out of $2 \sin (x) \cos (x)$ .

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

Step 1.3

Factor $\sin (x)$ out of $\sin (x) \cdot 1 + \sin (x) (2 \cos (x))$ .

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

Step 2

Simplify by multiplying through.

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Step 2.1

Apply the distributive property.

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

Step 2.2

Simplify the expression.

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Step 2.2.1

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

$\sin (x) + \sin (x) (2 \cos (x))$

Step 2.2.2

Rewrite using the commutative property of multiplication.

$\sin (x) + 2 \sin (x) \cos (x)$

Step 3

Apply the sine double-angle identity.

$\sin (x) + \sin (2 x)$