Question

Find the value of $\sin [{\tan }^{-1}(-\sqrt{3})+{\cos }^{-1}\left(\frac{-\sqrt{3}}{2}\right)]$

Answer 1

$\sin [{\tan }^{-1}(-\sqrt{3})+{\cos }^{-1}\left(\frac{-\sqrt{3}}{2}\right)]$

$=\sin [\frac{-\pi }{3}+\frac{5\pi }{6}]$

$=\sin [\frac{-2\pi }{6}+\frac{5\pi }{6}]$

$=\sin \left[\frac{-2\pi +5\pi }{6}\right]$

$=\sin \left[\frac{3\pi }{6}\right]$

$=\sin \left[\frac{\pi }{2}\right]=1$