The principal value tan−1⁡sin⁡−π2 is

The principal value $\tan^{- 1} \{\sin (- \frac{π}{2})\}$ is

A
$\frac{π}{4}$
B
$\frac{- π}{4}$
C
$\frac{3 π}{4}$
D
$\frac{- 3 π}{4}$

Solution:

We know that $\sin (- \frac{π}{2}) = - 1$

$\tan^{'} \{\sin (- \frac{π}{2})\} = \tan^{- 1} (- 1) = - \frac{π}{4}$

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