If ` 4 cos ^(2) A -3 =0 and 0^(@) le A le 90 ^(@) ` find :
angla A

Answer

To solve the equation \( 4 \cos^2 A - 3 = 0 \) for \( A \) in the range \( 0^\circ \leq A \leq 90^\circ \), follow these steps:

### Step 1: Rearrange the equation
Start by isolating \( \cos^2 A \):
\[ 4 \cos^2 A - 3 = 0 \]
Add 3 to both sides:
\[ 4 \cos^2 A = 3 \]

### Step 2: Divide by 4
Now, divide both sides by 4 to solve for \( \cos^2 A \):
\[ \cos^2 A = \frac{3}{4} \]

### Step 3: Take the square root
Next, take the square root of both sides to find \( \cos A \):
\[ \cos A = \sqrt{\frac{3}{4}} \quad \text{or} \quad \cos A = -\sqrt{\frac{3}{4}} \]
Since \( A \) is between \( 0^\circ \) and \( 90^\circ \), we only consider the positive root:
\[ \cos A = \frac{\sqrt{3}}{2} \]

### Step 4: Find the angle
Now, we need to find the angle \( A \) such that \( \cos A = \frac{\sqrt{3}}{2} \). We know that:
\[ \cos 30^\circ = \frac{\sqrt{3}}{2} \]
Thus, we can conclude:
\[ A = 30^\circ \]

### Final Answer
The value of angle \( A \) is:
\[ A = 30^\circ \]