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TS EAMCET · Maths · Inverse Trigonometric Functions

\(\tan ^{-1}\left(\frac{1}{2 \sqrt{2}}\right)+\sin ^{-1}\left(\frac{1}{\sqrt{3}}\right)=\cos ^{-1} x\), then \(x=\)

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

Answer & Solution

Correct Answer

(A) \(\frac{1}{\sqrt{3}}\)

Step-by-step Solution

Detailed explanation

We have, \(\tan ^{-1}\left(\frac{1}{2 \sqrt{2}}\right)+\sin ^{-1}\left(\frac{1}{\sqrt{3}}\right)=\cos ^{-1} x\). Let \(\theta_1=\tan ^{-1} \frac{1}{2 \sqrt{2}}\) and \(\theta_2=\sin ^{-1} \frac{1}{\sqrt{3}}\). Then,…