WBJEE · Maths · Trigonometric Equations
The trigonometric equation \(\sin ^{-1} x=2 \sin ^{-1} 2 a\) has a real solution, if
- A \(|a|>\frac{1}{\sqrt{2}}\)
- B \(\frac{1}{2 \sqrt{2}} < |a| < \frac{1}{\sqrt{2}}\)
- C \(|a|>\frac{1}{2 \sqrt{2}}\)
- D \(|a| \leq \frac{1}{2 \sqrt{2}}\)
Answer & Solution
Correct Answer
(D) \(|a| \leq \frac{1}{2 \sqrt{2}}\)
Step-by-step Solution
Detailed explanation
We know that, \(-\frac{\pi}{2} \leq \sin ^{-1} x \leq \frac{\pi}{2}\) \(\Rightarrow \frac{-\pi}{2} \leq 2 \sin ^{-1} 2 a \leq \frac{\pi}{2}\) \(\Rightarrow \frac{-\pi}{4} \leq \sin ^{-1} 2 a \leq \frac{\pi}{4}\)…
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