COMEDK · Maths · 23. Inverse Trigonometric Functions
\(\sin ^{-1}\left[x \sqrt{1-x}-\sqrt{x} \sqrt{1-x^{2}}\right]=\)
- A \(\sin ^{-1} x-\sin ^{-1} \sqrt{1-x^{2}}\)
- B \(\sin ^{-1} x+\sin ^{-1} \sqrt{1-x}\)
- C \(\sin ^{-1} x-\sin ^{1} \sqrt{x}\)
- D \(\sin ^{-1} x+\sin ^{-1} \sqrt{x}\)
Answer & Solution
Correct Answer
(C) \(\sin ^{-1} x-\sin ^{1} \sqrt{x}\)
Step-by-step Solution
Detailed explanation
Let, \(y=\sin ^{-1}\left[x \sqrt{1-x}-\sqrt{x} \sqrt{1-x^{2}}\right]\) \[ \begin{aligned} &=\sin ^{-1}\left[x \sqrt{1-(\sqrt{x})^{2}}-\sqrt{x} \sqrt{1-x^{2}}\right] \\ &=\sin ^{-1} x-\sin ^{-1} \sqrt{x} \end{aligned} \]…
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