The principal value $tan^{-1}\begin{Bmatrix}sin\left(-\frac{\pi}{2}\right)\end{Bmatrix},$ is
Answer & explanation
Correct answer: option 2
We know that $sin\left(-\frac{\pi}{2}\right) = -1.$
$tan^{-1}\begin{Bmatrix}sin\left(-\frac{\pi}{2}\right)\end{Bmatrix}=tan^{-1}(-1)=-\frac{\pi}{4}$