Question

4 sin A.sin^2 A +1 - 2 sin^2 A = 2 sin A. Find the value of A

Answer 1

see
=> 4 sinA. sin2 A +1 - 2sin2A = 2sin A
=> 4 sinA.sin2 A - 2sin 2A - 2sin A +1 =0
=> 2 sin 2A(2sin A -1) -1( 2sin A -1) =0
=> (2 sin 2A -1) ( 2 sin A -1) =0
now,
=> sinA =1/2, sin2A =1/2.
=> sinA =1/2. (sin 30 =1/2)
=> sin A = sin 30
=> A =30
now,
=> sin 2A =sin 30
=> 2A =30
=> A =15

answer A =15,30

Answer 2

Step-by-step explanation:

given

4 Sin A Sin 2A + 1 - 2 Sin 2A = 2 Sin A

4 Sin A 2 Sin A cosA + 1-2 ( 2 sinA cosA) = 2 sin A

8 Sin2 A CosA- 4 SinA cos A =2 Sin A-1

4 Sin A Cos A( 2 Sin A - 1)= 2 Sin A -1

4 sin A cos A=1

2 Sin 2A = 1

Sin24 = 1/2 = Sin 30

2A=30

A=15