The value of tan^{-1} 1+√3/3+√3 + sec^{-1} (8+4√3/6+3√3)^1/2 is

Question

The value of \(\tan^{-1} \frac{1 + \sqrt 3}{3 + \sqrt 3} + \sec^{-1} \left(\frac{8 + 4\sqrt 3}{6 + 3\sqrt 3}\right)^{1/2}\) is

(1) \(\frac \pi 4\)

(2) \(\frac \pi 6\)

(3) \(\frac \pi 5\)

(4) \(\frac \pi 3\)

Answer 1

Correct option is (4) \(\frac \pi 3\)