Trigonometry Examples

$\tan^{2} (3 x) - 2 \sin^{2} (3 x) = 0$

Step 1

Simplify $\tan^{2} (3 x) - 2 \sin^{2} (3 x)$ .

Tap for more steps...

Step 1.1

Simplify each term.

Tap for more steps...

Step 1.1.1

Rewrite $\tan (3 x)$ in terms of sines and cosines.

${(\frac{\sin (3 x)}{\cos (3 x)})}^{2} - 2 \sin^{2} (3 x) = 0$

Step 1.1.2

Apply the product rule to $\frac{\sin (3 x)}{\cos (3 x)}$ .

$\frac{\sin^{2} (3 x)}{\cos^{2} (3 x)} - 2 \sin^{2} (3 x) = 0$

Step 1.2

Convert from $\frac{\sin^{2} (3 x)}{\cos^{2} (3 x)}$ to $\tan^{2} (3 x)$ .

$\tan^{2} (3 x) - 2 \sin^{2} (3 x) = 0$

Step 2

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

$x = \frac{π n}{3}, \frac{π}{12} + \frac{π n}{3}, \frac{π}{4} + \frac{π n}{3}$ , for any integer $n$

Step 3