WBJEE · Maths · Inverse Trigonometric Functions
The number of solutions of \(\sin ^{-1} x+\sin ^{-1}(1-x)=\cos ^{-1} x\) is
- A \(0\)
- B \(1\)
- C \(2\)
- D \(4\)
Answer & Solution
Correct Answer
(C) \(2\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \sin ^{-1} x+\sin ^{-1}(1-x)=\cos ^{-1} x \\ & \Rightarrow 1-x=\sqrt{1-x} \sqrt{1-x}-x \cdot x \\ & \Rightarrow x=0 \text { or } 1 / 2\end{aligned}\)
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