Trigonometry Examples

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

Step 1

Simplify by multiplying through.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Simplify with commuting.

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Step 1.2.1

Reorder $2 \cos (x)$ and $\sin (x)$ .

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

Step 1.2.2

Reorder $\sin (x)$ and $2$ .

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

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

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

Step 2

Apply the sine double-angle identity.

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

Step 3

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

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

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$