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
- A \(\frac{3 \pi}{20}\)
- B \(\frac{17 \pi}{20}\)
- C \(\frac{7 \pi}{10}\)
- D \(\frac{\pi}{10}\)
Answer & Solution
Correct Answer
(B) \(\frac{17 \pi}{20}\)
Step-by-step Solution
Detailed explanation
\( \cos ^{-1}\left[\frac{1}{\sqrt{2}}\left(\cos \frac{9 \pi}{10}-\sin \frac{9 \pi}{10}\right)\right] = \cos ^{-1}\left[\cos \frac{\pi}{4} \cos \frac{9 \pi}{10}-\sin \frac{\pi}{4} \sin \frac{9 \pi}{10}\right] \) \( = \cos ^{-1}\left[\cos \left(\frac{\pi}{4}+\frac{9 \pi}{10}\right)\right] \)
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