Trigonometry Examples

$2 \cos (x) \sin (x) - 2 \cos (x) - \sqrt{3} \sin (x) + \sqrt{3} = 0$

Step 1

Simplify each term.

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Step 1.1

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

$\sin (x) (2 \cos (x)) - 2 \cos (x) - \sqrt{3} \sin (x) + \sqrt{3} = 0$

Step 1.2

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

$2 \cdot \sin (x) \cos (x) - 2 \cos (x) - \sqrt{3} \sin (x) + \sqrt{3} = 0$

Step 1.3

Apply the sine double-angle identity.

$\sin (2 x) - 2 \cos (x) - \sqrt{3} \sin (x) + \sqrt{3} = 0$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x = \frac{π}{6} + 2 π n, \frac{π}{2} + 2 π n, \frac{11 π}{6} + 2 π n$ , for any integer $n$

Step 3