If `tantheta=cottheta" and "0^(@) le theta le 90^(@)`, state the value of `theta`.

Answer

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

### Step 1: Understand the relationship between tangent and cotangent
Recall that \( \cot \theta \) is the reciprocal of \( \tan \theta \). Therefore, we can rewrite the equation:
\[ \tan \theta = \frac{1}{\tan \theta} \]

### Step 2: Multiply both sides by \( \tan \theta \)
To eliminate the fraction, we can multiply both sides of the equation by \( \tan \theta \) (assuming \( \tan \theta \neq 0 \)):
\[ \tan^2 \theta = 1 \]

### Step 3: Solve for \( \tan \theta \)
Taking the square root of both sides gives us:
\[ \tan \theta = 1 \quad \text{or} \quad \tan \theta = -1 \]
Since \( \theta \) is in the range \( 0^\circ \leq \theta \leq 90^\circ \), we only consider the positive value:
\[ \tan \theta = 1 \]

### Step 4: Find the angle \( \theta \)
The angle \( \theta \) for which \( \tan \theta = 1 \) is:
\[ \theta = 45^\circ \]

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

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