Calculate the value of A, if :
`(sinA-1)(2cosA-1)=0`

Answer

To solve the equation \((\sin A - 1)(2\cos A - 1) = 0\), we need to break it down into two separate equations based on the zero product property.

### Step-by-Step Solution:

1. **Set each factor to zero**:
\[ \sin A - 1 = 0 \quad \text{or} \quad 2\cos A - 1 = 0 \]

2. **Solve the first equation**:
\[ \sin A - 1 = 0 \implies \sin A = 1 \]
The sine function equals 1 at:
\[ A = 90^\circ \]

3. **Solve the second equation**:
\[ 2\cos A - 1 = 0 \implies 2\cos A = 1 \implies \cos A = \frac{1}{2} \]
The cosine function equals \(\frac{1}{2}\) at:
\[ A = 60^\circ \quad \text{and} \quad A = 300^\circ \quad (\text{in the range of } 0^\circ \text{ to } 360^\circ) \]

4. **Final values of A**:
The solutions to the original equation are:
\[ A = 90^\circ, 60^\circ, \text{ and } 300^\circ \]

### Summary of Solutions:
The values of \(A\) that satisfy the equation \((\sin A - 1)(2\cos A - 1) = 0\) are:
\[ A = 90^\circ, 60^\circ, 300^\circ \]