MHT CET · Maths · Inverse Trigonometric Functions
The value of \(\tan ^{-1}(-\sqrt{3})-\sin ^{-1}\left(\frac{1}{\sqrt{2}}\right)+\cos ^{-1}\left(\frac{-1}{2}\right)\) is
- A \(\frac{-\pi}{4}\)
- B \(\frac{4 \pi}{3}\)
- C \(\frac{\pi}{12}\)
- D \(\frac{7 \pi}{12}\)
Answer & Solution
Correct Answer
(C) \(\frac{\pi}{12}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \tan ^{-1}(-\sqrt{3})-\sin ^{-1}\left(\frac{1}{\sqrt{2}}\right)+\cos ^{-1}\left(-\frac{1}{2}\right) \\ & =-\tan ^{-1}(\sqrt{3})-\sin ^{-1}\left(\frac{1}{\sqrt{2}}\right)+\pi-\cos ^{-1}\left(\frac{1}{2}\right) \\ & =-\frac{\pi}{3}-\frac{\pi}{4}+\pi-\frac{\pi}{3}=\frac{\pi}{12}\end{aligned}\)
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