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 \(x=\)
- A \(\frac{1}{\sqrt{3}}\)
- B \(\frac{1}{\sqrt{2}}\)
- C \(\frac{2}{\sqrt{3}}\)
- D \(\frac{1}{2 \sqrt{2}}\)
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,…
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