Question

Write the principal value of $ta{n}^{-1}\left(1\right)+co{s}^{-1}(-\frac{1}{2})$

Answer 1

${\tan }^{-1}\left(1\right)+{\cos }^{-1}(-\frac{1}{2})$

$\Rightarrow \frac{\pi }{4}+\pi -{\cos }^{-1}\left(\frac{1}{2}\right)$

$\Rightarrow \frac{\pi }{4}+\pi -\frac{\pi }{3}$

$\Rightarrow \frac{3\pi +12\pi -4\pi }{12}$

$\Rightarrow \frac{11\pi }{12}$

Therefore, principle value of ${\tan }^{-1}\left(1\right)+{\cos }^{-1}(-\frac{1}{2})$ is $\frac{11\pi }{12}.$