# How do you evaluate tan^-1(sin(pi/2)) without a calculator?

${\tan}^{- 1} \left(\sin \left(\frac{\pi}{2}\right)\right) = \frac{\pi}{4}$
As $\sin \left(\frac{\pi}{2}\right) = 1$ and $\tan \left(\frac{\pi}{4}\right) = 1$
${\tan}^{- 1} \left(\sin \left(\frac{\pi}{2}\right)\right) = {\tan}^{- 1} 1 = \frac{\pi}{4}$