If `theta^(@) lt theta lt 90^(@)` and `(sin theta)/(cos theta) + (cos theta)/(sin theta)=2`, then which of the following is equal to `theta` ?

Options

A. `30^(@)`
B. `45^(@)`
C. `60^(@)`
D. `75^(@)`

Answer

To solve the problem, we need to simplify the equation given and find the value of \( \theta \).

### Step-by-Step Solution:

1. **Start with the given equation:**
\[ \frac{\sin \theta}{\cos \theta} + \frac{\cos \theta}{\sin \theta} = 2 \]

2. **Rewrite the left side using the identity for tangent and cotangent:**
\[ \tan \theta + \cot \theta = 2 \]

3. **Let \( x = \tan \theta \). Then, \( \cot \theta = \frac{1}{x} \):**
\[ x + \frac{1}{x} = 2 \]

4. **Multiply through by \( x \) to eliminate the fraction:**
\[ x^2 + 1 = 2x \]

5. **Rearrange the equation to form a quadratic equation:**
\[ x^2 - 2x + 1 = 0 \]

6. **Factor the quadratic:**
\[ (x - 1)^2 = 0 \]

7. **Solve for \( x \):**
\[ x - 1 = 0 \implies x = 1 \]

8. **Recall that \( x = \tan \theta \):**
\[ \tan \theta = 1 \]

9. **Find \( \theta \) by taking the arctangent:**
\[ \theta = \tan^{-1}(1) \]

10. **Since \( \tan 45^\circ = 1 \):**
\[ \theta = 45^\circ \]

### Conclusion:
The value of \( \theta \) is \( 45^\circ \).