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Home » Mark the tick against the correct answer in the following: The principal value of is A. B. C. D. none of these
Mark the tick against the correct answer in the following: The principal value of \tan ^{-1}(-\sqrt{3}) is
A. \frac{2 \pi}{3}
B. \frac{4 \pi}{3}
C. \frac{-\pi}{3}
D. none of these
CBSE | Class 12 | Inverse Trigonometric Functions | Maths | RS Aggarwal
Mark the tick against the correct answer in the following: The principal value of \tan ^{-1}(-\sqrt{3}) is
A. \frac{2 \pi}{3}
B. \frac{4 \pi}{3}
C. \frac{-\pi}{3}
D. none of these

Solution:

Option(C) is correct.
To Find: The Principle value of \tan ^{-1}(-\sqrt{3})
Let the principle value be given by x
Now, let x=\tan ^{-1}(-\sqrt{3})
\begin{array}{l} \Rightarrow \tan x=-\sqrt{3} \\ \Rightarrow \tan x=-\tan \left(\frac{\pi}{3}\right)\left(\because \tan \left(\frac{\pi}{3}\right)=-\sqrt{3}\right) \\ \Rightarrow \tan x=\tan \left(-\frac{\pi}{3}\right)(\because-\tan (\theta)=\tan (-\theta)) \\ \Rightarrow x=-\frac{\pi}{3} \end{array}

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