TS EAMCET · Maths · Inverse Trigonometric Functions
The value of \(x\) which satisfies \(\sin \left(\cot ^{-1} x\right)=\cos \left(\tan ^{-1}(1+x)\right)\) is
- A \(-\frac{1}{2}\)
- B \(\frac{1}{2}\)
- C -1
- D 1
Answer & Solution
Correct Answer
(A) \(-\frac{1}{2}\)
Step-by-step Solution
Detailed explanation
Given, \(\sin \left(\cot ^{-1} x\right)=\cos \left[\tan ^{-1}(1+x)\right]\) And we know that, \(\cot ^{-1} \theta=\sin ^{-1}\left(\frac{1}{\sqrt{1+\theta^2}}\right)\) and \(\tan ^{-1} \theta=\cos ^{-1}\left(\frac{1}{\sqrt{1+\theta^2}}\right)\) \(\therefore\) From Eq. (i), we get…
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