KCET · Maths · Inverse Trigonometric Functions
\(\cos \left(2 \cos ^{-1} \frac{1}{5}+\sin ^{-1} \frac{1}{5}\right)\) is euqal to
- A \(\frac{1}{5}\)
- B \(\frac{-2 \sqrt{6}}{5}\)
- C \(-\frac{1}{5}\)
- D \(\frac{\sqrt{6}}{5}\)
Answer & Solution
Correct Answer
(B) \(\frac{-2 \sqrt{6}}{5}\)
Step-by-step Solution
Detailed explanation
\( \cos \left(2 \cos ^{-1} \frac{1}{5}+\sin ^{-1} \frac{1}{5}\right) = \cos \left(\cos ^{-1} \frac{1}{5} + \left(\cos ^{-1} \frac{1}{5}+\sin ^{-1} \frac{1}{5}\right)\right) \) \( = \cos \left(\cos ^{-1} \frac{1}{5} + \frac{\pi}{2}\right) \)
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