`sectheta.cottheta=cosectheta`, write true or false.

Answer

To determine whether the statement \( \sec \theta \cdot \cot \theta = \csc \theta \) is true or false, we will evaluate the left-hand side (LHS) and see if it equals the right-hand side (RHS).

### Step-by-step Solution:

1. **Identify the LHS:**
\[ \text{LHS} = \sec \theta \cdot \cot \theta \]

2. **Substitute the definitions of secant and cotangent:**
- Recall that:
\[ \sec \theta = \frac{1}{\cos \theta} \]
\[ \cot \theta = \frac{\cos \theta}{\sin \theta} \]
- Substitute these into the LHS:
\[ \text{LHS} = \frac{1}{\cos \theta} \cdot \frac{\cos \theta}{\sin \theta} \]

3. **Simplify the expression:**
- Multiply the fractions:
\[ \text{LHS} = \frac{1 \cdot \cos \theta}{\cos \theta \cdot \sin \theta} = \frac{1}{\sin \theta} \]

4. **Recognize the definition of cosecant:**
- We know that:
\[ \csc \theta = \frac{1}{\sin \theta} \]
- Therefore, we can write:
\[ \text{LHS} = \csc \theta \]

5. **Compare LHS and RHS:**
- Since we have shown that:
\[ \text{LHS} = \csc \theta \]
- The right-hand side (RHS) is also:
\[ \text{RHS} = \csc \theta \]

6. **Conclusion:**
- Since LHS equals RHS, we conclude that:
\[ \sec \theta \cdot \cot \theta = \csc \theta \quad \text{is true.} \]

### Final Answer:
**True**