If `sin theta - cos theta =0, 0 le theta le 90^(@)` then the value of `theta` is _____-

Answer

To solve the equation \( \sin \theta - \cos \theta = 0 \) for \( 0 \leq \theta \leq 90^\circ \), we can follow these steps:

### Step 1: Set up the equation
We start with the given equation:
\[ \sin \theta - \cos \theta = 0 \]

### Step 2: Rearrange the equation
We can rearrange this equation to isolate one of the trigonometric functions:
\[ \sin \theta = \cos \theta \]

### Step 3: Use the property of sine and cosine
The sine and cosine functions are equal at specific angles. In the interval \( 0 \leq \theta \leq 90^\circ \), this occurs when:
\[ \theta = 45^\circ \]

### Step 4: Verify the solution
To verify, we can substitute \( \theta = 45^\circ \) back into the original equation:
\[ \sin 45^\circ = \cos 45^\circ \]
Both \( \sin 45^\circ \) and \( \cos 45^\circ \) equal \( \frac{1}{\sqrt{2}} \), confirming that our solution is correct.

### Final Answer
Thus, the value of \( \theta \) is:
\[ \theta = 45^\circ \]

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