JEE Mains · Maths · STD 12 - 2. inverse trigonometric function
Considering the principal values of the inverse trigonometric functions, the sum of all the solutions of the equation \(\cos ^{-1}(x)-2 \sin ^{-1}(x)=\cos ^{-1}(2 x)\) is equal to.
- A \(0\)
- B \(1\)
- C \(\frac{1}{2}\)
- D \(-\frac{1}{2}\)
Answer & Solution
Correct Answer
(A) \(0\)
Step-by-step Solution
Detailed explanation
\(\cos ^{-1} x - 2 \sin ^{-1} x=\cos ^{-1} 2 x\) \(\cos ^{-1} x-2\left(\frac{\pi}{2}-\cos ^{-1} x\right)=\cos ^{-1} 2 x\) \(\cos ^{-1} x-\pi+2 \cos ^{-1} x=\cos ^{-1} 2 x\) \(3 \cos ^{-1} x=\pi+\cos ^{-1} 2 x\)…
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