If `4sin^(2)x^(@)-3=0" and "x^(@)` is an acute angle, find :
(i) `sinx^(@) " (ii) "x^(@)`

Answer

To solve the equation \( 4\sin^2 x^\circ - 3 = 0 \) and find the values of \( \sin x^\circ \) and \( x^\circ \), we can follow these steps:

### Step 1: Rearrange the Equation
We start with the equation:
\[ 4\sin^2 x^\circ - 3 = 0 \]
Add 3 to both sides:
\[ 4\sin^2 x^\circ = 3 \]

### Step 2: Divide by 4
Next, divide both sides by 4:
\[ \sin^2 x^\circ = \frac{3}{4} \]

### Step 3: Take the Square Root
Now, take the square root of both sides:
\[ \sin x^\circ = \sqrt{\frac{3}{4}} \]
This simplifies to:
\[ \sin x^\circ = \frac{\sqrt{3}}{2} \]
Since \( x^\circ \) is an acute angle, we take the positive root.

### Step 4: Find the Angle
We know that \( \sin 60^\circ = \frac{\sqrt{3}}{2} \). Therefore, we can conclude:
\[ x^\circ = 60^\circ \]

### Final Answers
(i) \( \sin x^\circ = \frac{\sqrt{3}}{2} \)
(ii) \( x^\circ = 60^\circ \)

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