If A and B are Acute Positive Angles Satisfying The Equation 3 Sin2 A + 2 Sin2B = 1 And 3 Sin 2A – 2 Sin2B = 0, Then A + 2B is Equal To

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Question

easy

Correct option is

π/2

From the given relations, we have

sin 2B = (3/2) sin 2A and

3 sin² A = 1 – 2 sin² B = cos 2B

so that

cos (A + 2B) = cos A cos 2B – sin A sin 2B

= cos A.3 sin²A – (3/2) sin A sin 2A

= 3 cos A sin²A – 3 sin²A cos A = 0

⇒ A + 2B = π/2.