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

The Correct Option is A

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): \(\frac {\pi}{3}\)