﻿ 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   : Kaysons Education

# 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

### Solution

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.

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