Trigonometry Examples

$\frac{\sin (2 x)}{\cos (x)} = 2 \sin (x)$

Step 1

Simplify $\frac{\sin (2 x)}{\cos (x)}$ .

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Step 1.1

Apply the sine double-angle identity.

$\frac{2 \sin (x) \cos (x)}{\cos (x)} = 2 \sin (x)$

Step 1.2

Cancel the common factor of $\cos (x)$ .

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Step 1.2.1

Cancel the common factor.

$\frac{2 \sin (x) \cos (x)}{\cos (x)} = 2 \sin (x)$

Step 1.2.2

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

$2 \sin (x) = 2 \sin (x)$

Step 2

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

$x \approx 0.1, - \frac{1}{5}, \frac{1}{5}, 0.3, - \frac{2}{5}, \frac{2}{5}, - \frac{1}{2}$

Step 3