If `sinx =cosx` and x is acute, state the value of x.

Answer

To solve the equation \( \sin x = \cos x \) for an acute angle \( x \), we can follow these steps:

### Step 1: Start with the given equation
We have:
\[ \sin x = \cos x \]

### Step 2: Divide both sides by \( \cos x \)
To manipulate the equation, we can divide both sides by \( \cos x \) (assuming \( \cos x \neq 0 \)):
\[ \frac{\sin x}{\cos x} = 1 \]

### Step 3: Recognize the left side as the tangent function
The left side of the equation can be expressed as:
\[ \tan x = 1 \]

### Step 4: Find the angle for which the tangent is 1
We know that the tangent of an angle is equal to 1 at:
\[ x = 45^\circ \]

### Step 5: State the final answer
Since \( x \) is an acute angle, the value of \( x \) is:
\[ \boxed{45^\circ} \]

---