Question

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

(Please explain steps)

Answer 1

The answer is "
`\bold{(\pi)/(6)}`"

Explanation:

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

`\to 3 (\sin x)/(\cos x) = 2 2\sin x \cos x \\\\\to 3 (\sin x)/(\cos x) = 4\sin x \cos x \\\\\to (\sin x)/(\cos x \sin x \cos x ) = (4)/(3) \\\\\to (1)/(\cos^2 x ) = (4)/(3) \\\\\to \sec^2 x = (4)/(3) \\\\\to \sec x = (2)/(√(3)) \\\\\to \sec x= \sec (\pi)/(6) \\\\ \to x= (\pi)/(6)`