Mathematics - Inverse Trigonometric Functions Question with Solution | TestHub

${\tan }^{-1}\left(\frac{1+\sqrt{3}}{3+\sqrt{3}}\right)+{\sec }^{-1}\sqrt{\frac{8+4\sqrt{3}}{6+3\sqrt{3}}}$

$={\tan }^{-1}\left(\frac{1+\sqrt{3}}{\sqrt{3}\left(1+\sqrt{3}\right)}\right)+{\sec }^{-1}\sqrt{\frac{4\left(2+\sqrt{3}\right)}{3\left(2+\sqrt{3}\right)}}$

$={\tan }^{-1}\left(\frac{1}{\sqrt{3}}\right)+{\sec }^{-1}\sqrt{\frac{4}{3}}$

$={\tan }^{-1}\left(\frac{1}{\sqrt{3}}\right)+{\cos }^{-1}\frac{\sqrt{3}}{2}=\frac{\mathrm{\pi }}{6}+\frac{\mathrm{\pi }}{6}=\frac{\mathrm{\pi }}{3}$