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AP EAMCET · Maths · Trigonometric Ratios & Identities

If \(A\) and \(B\) are positive 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 \(A+2 B=\)

  1. A \(30^{\circ}\)
  2. B \(45^{\circ}\)
  3. C \(60^{\circ}\)
  4. D \(90^{\circ}\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(90^{\circ}\)

Step-by-step Solution

Detailed explanation

\(\frac{3 \sin A}{\sin B}=\frac{2 \cos B}{\cos A} \implies 3 \sin A \cos A = 2 \sin B \cos B \implies \frac{3}{2} \sin(2A) = \sin(2B)\) (1) \(3 \cos ^2 A+2 \cos ^2 B=4 \implies 3\left(\frac{1+\cos(2A)}{2}\right) + 2\left(\frac{1+\cos(2B)}{2}\right) = 4\)…