AP EAMCET · Maths · Inverse Trigonometric Functions
If \(\cos ^{-1} x=\sin ^{-1}(3 x)\), then \(x\) is equal to
- A \(\frac{\sqrt{10}}{10}\)
- B \(\frac{\sqrt{5}}{5}\)
- C \(\frac{5}{2 \sqrt{6}}\)
- D \(\frac{-\sqrt{10}}{10}\)
Answer & Solution
Correct Answer
(A) \(\frac{\sqrt{10}}{10}\)
Step-by-step Solution
Detailed explanation
Given, \(\cos ^{-1} x=\sin ^{-1} 3 x\) \(\begin{aligned} \Rightarrow \sin ^{-1}\left(\sqrt{1-x^2}\right)= & \sin ^{-1} 3 x \\ & {\left[\because \cos ^{-1} x=\sin ^{-1} \sqrt{1-x^2}\right] }\end{aligned}\)…
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