JEE Mains · Maths · STD 12 - 2. inverse trigonometric function
Given that the inverse trigonometric functions take principal values only. Then, the number of real values of \(x\) which satisfy \(\sin ^{-1}\left(\frac{3 x}{5}\right)+\sin ^{-1}\left(\frac{4 x}{5}\right)=\sin ^{-1} x\) is equal to:
- A \(2\)
- B \(1\)
- C \(3\)
- D \(0\)
Answer & Solution
Correct Answer
(C) \(3\)
Step-by-step Solution
Detailed explanation
\(\sin ^{-1} \frac{3 x}{5}+\sin ^{-1} \frac{4 x}{5}=\sin ^{-1} x\) \(\sin ^{-1}\left(\frac{3 x}{5} \sqrt{1-\frac{16 x^{2}}{25}}+\frac{4 x}{5} \sqrt{1-\frac{9 x^{2}}{25}}\right)=\sin ^{-1} x\)…
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