Question

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

 

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.

SIMILAR QUESTIONS

Q1

  

 

Q2

The expression

             

Q3

If tan (π cos θ) = cot (π sin θ) then cos (θ – π/4) is equal to

Q4

 

 

 

Q5

If sin A, cos A and tan A are in geometric progression, then cot6 A – cot2 is equal to

 

Q7

If the value of

        

Is equal to k2, then k is equal to

Q8

  is equal to

 

Q9

 of k is equal to

 

Q10

  equal to