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COMEDK · Maths · 23. Inverse Trigonometric Functions

\(\sin \left[2 \cos ^{-1} \cot \left(2 \tan ^{-1} \frac{1}{2}\right)\right]\) is equal to

  1. A \(\frac{3 \sqrt{7}}{8}\)
  2. B \(\frac{5 \sqrt{7}}{8}\)
  3. C \(\frac{5 \sqrt{7}}{2}\)
  4. D \(\frac{3 \sqrt{7}}{2}\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{3 \sqrt{7}}{8}\)

Step-by-step Solution

Detailed explanation

\(=\sin \left[2 \cos ^{-1}\left\{\cot \left(\tan ^{-1} \frac{1}{1-\frac{1}{4}}\right)\right\}\right]\) \(=\sin \left[2 \cos ^{-1}\left\{\cot \left(\tan ^{-1} \frac{\frac{4}{3}}{3}\right)\right\}\right]\) \(=\sin \left[2 \cos ^{-1} \frac{3}{\frac{4}{4}}\right]=\sin 20\)…