Correct Answer: Option C

Explanation

tan x = \(\frac{2}{3}\)(given), is illustrated in a right-angled \(\Delta\)

thus m² = 2² + 3²

= 4 + 9 = 13

m = \(\sqrt{13}\)

Hence, 2sin x = 2 x \(\frac{2}{m}\)

2 x\(\frac{2}{\sqrt{13}}\)

= \(\frac{4}{\sqrt{13}}\)

= \(\frac{4}{\sqrt{13}} = \frac{\sqrt{13}}{\sqrt{13}}\)

= \(\frac{4\sqrt{13}}{13}\)

There is an explanation video available below.

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