AP EAMCET · Maths · Trigonometric Ratios & Identities
If \(A\) and \(B\) are acute angles satisfying \(3 \cos ^2 A+2 \cos ^2 B=4\) and \(\frac{3 \sin A}{\sin B}=\frac{2 \cos B}{\cos A}\), then \(A+2 B=\)
- A \(\frac{\pi}{2}\)
- B \(\frac{\pi}{3}\)
- C \(\frac{\pi}{4}\)
- D \(\frac{\pi}{6}\)
Answer & Solution
Correct Answer
(A) \(\frac{\pi}{2}\)
Step-by-step Solution
Detailed explanation
\(3 \sin A \cos A = 2 \sin B \cos B \implies \frac{3}{2} \sin 2A = \sin 2B\) \(3 \left(\frac{1+\cos 2A}{2}\right) + 2 \left(\frac{1+\cos 2B}{2}\right) = 4 \implies 3+3 \cos 2A + 2+2 \cos 2B = 8 \implies 3 \cos 2A + 2 \cos 2B = 3\) Substitute \(\sin 2B = \frac{3}{2} \sin 2A\) and…
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