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  4. The value of the expresion tan ( cos -1 (1/2)+ tan -1((-1/√3))), is equal to

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Q. The value of the expresion $\tan \left(\cos ^{-1} \frac{1}{2}+\tan ^{-1}\left(\frac{-1}{\sqrt{3}}\right)\right)$, is equal to

Inverse Trigonometric Functions

Solution:

$\tan \left(\cos ^{-1} \frac{1}{2}+\tan ^{-1}\left(\frac{-1}{\sqrt{3}}\right)\right)=\tan \left(\frac{\pi}{3}-\frac{\pi}{6}\right)=\tan \left(\frac{\pi}{6}\right)=\frac{1}{\sqrt{3}}$.