QuestionFor Ecercises 29-32, find the exeact value. (31) $2 \cos ^{-1}\left(-\frac{\sqrt{3}}{2}\right)-\tan ^{-1} \frac{\sqrt{3}}{3}$

Studdy Solution
Substitute the values into the expression and simplify:
$$2 \cos^{-1}\left(-\frac{\sqrt{3}}{2}\right) - \tan^{-1}\left(\frac{\sqrt{3}}{3}\right)$$
Substitute the evaluated values:
$$2 \times \frac{5\pi}{6} - \frac{\pi}{6}$$
Calculate:
$$\frac{10\pi}{6} - \frac{\pi}{6} = \frac{9\pi}{6} = \frac{3\pi}{2}$$
The exact value of the expression is:
$$\boxed{\frac{3\pi}{2}}$$