Question

3tan(x) = 2sin(2x) from [0,2 pi)

(Please explain steps)

Answer 1

Answer:

The answer is "$\bold{\frac{\pi}{6}}$"

Step-by-step explanation:

$\to 3 \tan(x) = 2 \sin(2x)$

$\to 3 \frac{\sin x}{\cos x} = 2 2\sin x \cos x \\\\\to 3 \frac{\sin x}{\cos x} = 4\sin x \cos x \\\\\to \frac{\sin x}{\cos x \sin x \cos x } = \frac{4}{3} \\\\\to \frac{1}{\cos^2 x } = \frac{4}{3} \\\\\to \sec^2 x = \frac{4}{3} \\\\\to \sec x = \frac{2}{\sqrt{3}} \\\\\to \sec x= \sec \frac{\pi}{6} \\\\ \to x= \frac{\pi}{6}$