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MHT CET · Maths · Inverse Trigonometric Functions

The principal value of \(\cos ^{-1}\left[\frac{1}{\sqrt{2}}\left(\cos \frac{9 \pi}{10}-\sin \frac{9 \pi}{10}\right)\right]\) is

  1. A \(\frac{3 \pi}{20}\)
  2. B \(\frac{17 \pi}{20}\)
  3. C \(\frac{7 \pi}{10}\)
  4. D \(\frac{\pi}{10}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{17 \pi}{20}\)

Step-by-step Solution

Detailed explanation

\( \cos ^{-1}\left[\frac{1}{\sqrt{2}}\left(\cos \frac{9 \pi}{10}-\sin \frac{9 \pi}{10}\right)\right] = \cos ^{-1}\left[\cos \frac{\pi}{4} \cos \frac{9 \pi}{10}-\sin \frac{\pi}{4} \sin \frac{9 \pi}{10}\right] \) \( = \cos ^{-1}\left[\cos \left(\frac{\pi}{4}+\frac{9 \pi}{10}\right)\right] \)