MHT CET · Maths · Inverse Trigonometric Functions
\(\tan ^{-1}\left(\tan \frac{5 \pi}{6}\right)+\cos ^{-1}\left(\cos \frac{13 \pi}{6}\right)=\)
- A 0
- B \(3 \pi\)
- C \(\frac{-\pi}{6}\)
- D \(\frac{\pi}{6}\)
Answer & Solution
Correct Answer
(A) 0
Step-by-step Solution
Detailed explanation
\(\tan ^{-1}\left(\tan \frac{5 \pi}{6}\right)+\cos ^{-1}\left(\cos \frac{13 \pi}{6}\right) \)
\( =\tan ^{-1}\left[\tan \left(\pi-\frac{\pi}{6}\right)\right]+\cos ^{-1}\left[\cos \left(2 \pi+\frac{\pi}{6}\right)\right] \)
\( =\tan ^{-1}\left[-\tan \frac{\pi}{6}\right]+\cos ^{-1}\left[\cos \left(\frac{\pi}{6}\right)\right] \)
\( =\tan ^{-1}\left[\tan \left(-\frac{\pi}{6}\right)\right]+\cos ^{-1}\left[\cos \left(\frac{\pi}{6}\right)\right]\) \(=-\frac{\pi}{6}+\frac{\pi}{6}=0\)
\( =\tan ^{-1}\left[\tan \left(\pi-\frac{\pi}{6}\right)\right]+\cos ^{-1}\left[\cos \left(2 \pi+\frac{\pi}{6}\right)\right] \)
\( =\tan ^{-1}\left[-\tan \frac{\pi}{6}\right]+\cos ^{-1}\left[\cos \left(\frac{\pi}{6}\right)\right] \)
\( =\tan ^{-1}\left[\tan \left(-\frac{\pi}{6}\right)\right]+\cos ^{-1}\left[\cos \left(\frac{\pi}{6}\right)\right]\) \(=-\frac{\pi}{6}+\frac{\pi}{6}=0\)
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