Question

The Value of tan⁻¹ [2sin{2cos⁻¹ ($\frac {\sqrt 3}{2}$)}].

• A. $\frac {\pi}{3}$
• B. $\frac {2\pi}{3}$
• C. $\frac {-\pi}{3}$
• D. $\frac {\pi}{6}$

Answer 1

Answer: (A)

$\frac {\pi}{3}$

Answer 2

tan⁻¹ [2sin {2cos⁻¹ ($\frac {\sqrt 3}{2}$)}]
= tan⁻¹ [2sin {2cos⁻¹ (cos $\frac {\pi}{6}$)}]
= tan⁻¹ [2sin {2 x ($\frac {\pi}{6}$)}]
= tan⁻¹ [2sin ($\frac {\pi}{3}$)]
= tan⁻¹ [2 x $\frac {\sqrt 3}{2}$]
= tan⁻¹ ($\sqrt 3$)
= $\frac {\pi}{3}$

So, the correct option is (A): $\frac {\pi}{3}$