Question

Find the values of the following :
${\tan }^{-1}\left(1\right)+{\cos }^{-1}(-\frac{1}{2})+{\sin }^{-1}(-\frac{1}{2})$

Answer 1

${\tan }^{-1}\left(1\right)+\left\{{\cos }^{-1}\right(-\frac{1}{2})+{\sin }^{-1}(-\frac{1}{2}\left)\right\}$
since ${\cos }^{-1}x+si{n}^{-1}x=\frac{\pi }{2}$
$\Rightarrow {\tan }^{-1}\left(1\right)+\frac{\pi }{2}$
${\tan }^{-1}\left(1\right)=\frac{\pi }{4}$
$\Rightarrow \frac{\pi }{4}+\frac{\pi }{2}=\frac{3\pi }{4}$