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# What is the principal value of $$\cos^{-1} \bigg( -\large\frac{\sqrt 3}{2} \bigg).$$

• $$cos(\pi-\theta)=-cos\theta$$
We know that $$cos\frac{\pi}{6}=\frac{\sqrt3}{2}$$
$$\Rightarrow\:-\frac{\sqrt3}{2}=cos(\pi-\frac{\pi}{6})=cos\frac{5\pi}{6}$$
$$\Rightarrow\: \cos^{-1}-\frac{\sqrt3}{2}=cos^{-1}cos \bigg( \pi-\large\frac{\pi}{6} \bigg)=\large\frac{5\pi}{6}$$