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KCET · Maths · Inverse Trigonometric Functions

\(\tan ^{-1}\left[\frac{1}{\sqrt{3}} \sin \frac{5 \pi}{2}\right] +\sin ^{-1}\left[\cos \left(\sin ^{-} \frac{\sqrt{3}}{2}\right)\right]\) is equal to

  1. A 0
  2. B \(\frac{\pi}{6}\)
  3. C \(\frac{\pi}{3}\)
  4. D \(\pi\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\frac{\pi}{3}\)

Step-by-step Solution

Detailed explanation

\(\tan ^{-1}\left[\frac{1}{\sqrt{3}} \sin \frac{5 \pi}{2}\right] = \tan ^{-1}\left[\frac{1}{\sqrt{3}} \cdot 1\right] = \frac{\pi}{6}\) \(\sin ^{-1}\left[\cos \left(\sin ^{-1} \frac{\sqrt{3}}{2}\right)\right] = \sin ^{-1}\left[\cos \left(\frac{\pi}{3}\right)\right] = \sin ^{-1}\left[\frac{1}{2}\right] = \frac{\pi}{6}\)