[tex]\cos (\sin ^{-1}(-\frac{1}{2}))+\tan ^{-1}(\cos (\pi))[/tex]
First, let's find the values of:
[tex]\begin{gathered} \sin ^{-1}(-\frac{1}{2})=-30 \\ \cos (\pi)=-1 \end{gathered}[/tex]
So:
[tex]\cos (-30)+\tan ^{-1}(-1)=\frac{\sqrt[]{3}}{2}-\frac{\pi}{4}=\frac{4\sqrt[]{3}-2\pi}{8}=\frac{2(2\sqrt[]{3}-\pi)}{2(4)}[/tex]
Simplify:
Answer:
[tex]\frac{2\sqrt[]{3}-\pi}{4}[/tex]
