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KCET · Maths · Inverse Trigonometric Functions

\(\cos \left(2 \cos ^{-1} \frac{1}{5}+\sin ^{-1} \frac{1}{5}\right)\) is euqal to

  1. A \(\frac{1}{5}\)
  2. B \(\frac{-2 \sqrt{6}}{5}\)
  3. C \(-\frac{1}{5}\)
  4. D \(\frac{\sqrt{6}}{5}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{-2 \sqrt{6}}{5}\)

Step-by-step Solution

Detailed explanation

\( \cos \left(2 \cos ^{-1} \frac{1}{5}+\sin ^{-1} \frac{1}{5}\right) = \cos \left(\cos ^{-1} \frac{1}{5} + \left(\cos ^{-1} \frac{1}{5}+\sin ^{-1} \frac{1}{5}\right)\right) \) \( = \cos \left(\cos ^{-1} \frac{1}{5} + \frac{\pi}{2}\right) \)