WBJEE · Maths · Trigonometric Equations
If \(A\) and \(B\) are acute angles such that \(\sin A=\sin ^2 B\) and \(2 \cos ^2 A=3 \cos ^2 B\), then \((A, B)=\)
- A \(\left(\frac{\pi}{6}, \frac{\pi}{4}\right)\)
- B \(\left(\frac{\pi}{6}, \frac{\pi}{6}\right)\)
- C \(\left(\frac{\pi}{4}, \frac{\pi}{6}\right)\)
- D \(\left(\frac{\pi}{4}, \frac{\pi}{4}\right)\)
Answer & Solution
Correct Answer
(A) \(\left(\frac{\pi}{6}, \frac{\pi}{4}\right)\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text { Hint : } 2 \cos ^2 A=3\left(1-\sin ^2 B\right) \\ & \Rightarrow 2-2 \sin ^2 A=3-3 \sin A \quad\left(\because \sin ^2 B=\sin A\right)\end{aligned}\)…
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