KCET · Maths · Inverse Trigonometric Functions
The value of \( \sin ^{-1}\left(\cos \frac{53 \pi}{5}\right) \) is
- A \( 3 \frac{\pi}{5} \)
- B \(-3 \frac{\pi}{5} \)
- C \( \frac{\pi}{10} \)
- D \( -\frac{\pi}{10} \)
Answer & Solution
Correct Answer
(D) \( -\frac{\pi}{10} \)
Step-by-step Solution
Detailed explanation
\( \cos \frac{53 \pi}{5} = \cos \left(10 \pi + \frac{3 \pi}{5}\right) = \cos \frac{3 \pi}{5} \) \( \cos \frac{3 \pi}{5} = \sin \left(\frac{\pi}{2} - \frac{3 \pi}{5}\right) \)
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