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 can break it down into two separate equations:

1. \(\sin A - 1 = 0\)
2. \(2 \cos A - 1 = 0\)

### Step 1: Solve the first equation
From the first equation, we have:
\[ \sin A - 1 = 0 \]
This simplifies to:
\[ \sin A = 1 \]

### Step 2: Find the angle A
The sine function equals 1 at:
\[ A = 90^\circ \]

### Step 3: Solve the second equation
Now, we move to the second equation:
\[ 2 \cos A - 1 = 0 \]
This simplifies to:
\[ 2 \cos A = 1 \]
Dividing both sides by 2 gives:
\[ \cos A = \frac{1}{2} \]

### Step 4: Find the angle A
The cosine function equals \(\frac{1}{2}\) at:
\[ A = 60^\circ \quad \text{and} \quad A = 300^\circ \quad (\text{in the range of } 0^\circ \text{ to } 360^\circ) \]

### Final Solution
Thus, the values of \(A\) that satisfy the original equation are:
\[ A = 90^\circ \quad \text{and} \quad A = 60^\circ \]

---