If `sintheta-costheta=0, 0ltthetale90^@`, then the value of `theta` is:

Options

A. `90^@`
B. `60^@`
C. `45^@`
D. `30^@`

Answer

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

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

### Step 2: Rearrange the equation
Rearranging gives us:
\[ \sin \theta = \cos \theta \]

### Step 3: Use the identity for sine and cosine
We know that \( \sin \theta = \cos \theta \) occurs when \( \theta \) is \( 45^\circ \) because at this angle, both sine and cosine values are equal.

### Step 4: Verify the solution
To verify:
- Calculate \( \sin 45^\circ \) and \( \cos 45^\circ \):
\[ \sin 45^\circ = \frac{1}{\sqrt{2}}, \quad \cos 45^\circ = \frac{1}{\sqrt{2}} \]
- Substitute back into the equation:
\[ \sin 45^\circ - \cos 45^\circ = \frac{1}{\sqrt{2}} - \frac{1}{\sqrt{2}} = 0 \]

### Conclusion
Since the equation holds true, the value of \( \theta \) is:
\[ \theta = 45^\circ \]

### Final Answer
Thus, the value of \( \theta \) is \( 45^\circ \).

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