Find the magnitude of angle A, if :
`4sinAsin2A+1-2sin2A=2sinA`

Answer

To solve the equation \( 4 \sin A \sin 2A + 1 - 2 \sin 2A = 2 \sin A \), we will follow these steps:

### Step 1: Rearranging the Equation
We start by rearranging the equation to group similar terms together:
\[ 4 \sin A \sin 2A - 2 \sin A = 2 \sin 2A - 1 \]

### Step 2: Factoring Out Common Terms
Next, we can factor out \( 2 \sin A \) from the left side:
\[ 2 \sin A (2 \sin 2A - 1) = 2 \sin 2A - 1 \]

### Step 3: Simplifying the Equation
Now, we can simplify the equation by dividing both sides by \( 2 \sin 2A - 1 \) (assuming \( 2 \sin 2A - 1 \neq 0 \)):
\[ 2 \sin A = 1 \]

### Step 4: Solving for \( \sin A \)
Now, we isolate \( \sin A \):
\[ \sin A = \frac{1}{2} \]

### Step 5: Finding the Angle \( A \)
The value of \( A \) for which \( \sin A = \frac{1}{2} \) is:
\[ A = 30^\circ \quad \text{(since \( \sin 30^\circ = \frac{1}{2} \))} \]

### Final Answer
Thus, the magnitude of angle \( A \) is:
\[ \boxed{30^\circ} \]