Calculate: $\;$ $\tan^{-1}\left(1\right) + \cos^{-1} \left(\dfrac{-1}{2}\right) + \sin^{-1} \left(\dfrac{-1}{2}\right)$
Given: $\;$ $\tan^{-1}\left(1\right) + \cos^{-1} \left(\dfrac{-1}{2}\right) + \sin^{-1} \left(\dfrac{-1}{2}\right)$
$= \dfrac{\pi}{4} + \dfrac{\pi}{2} = \dfrac{3 \pi}{4}$
$\left\{\because \; \sin^{-1} x + \cos^{-1} x = \dfrac{\pi}{2}, \; \forall \; x \in \left[-1, 1\right]\right\}$ $\;$ [Cofunction Inverse Identity]