Find the value of angle A , if :
sin 2A = 1

Answer

To find the value of angle A given that \( \sin 2A = 1 \), we can follow these steps:

### Step 1: Set up the equation
We start with the equation:
\[ \sin 2A = 1 \]

### Step 2: Identify the angle for which sine is 1
We know that the sine function equals 1 at specific angles. The primary angle where this occurs is:
\[ \sin 90^\circ = 1 \]
Thus, we can equate:
\[ 2A = 90^\circ \]

### Step 3: Solve for angle A
To find angle A, we divide both sides of the equation by 2:
\[ A = \frac{90^\circ}{2} = 45^\circ \]

### Conclusion
Therefore, the value of angle A is:
\[ A = 45^\circ \]

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