`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 can follow these steps:

### Step 1: Write down the left-hand side (LHS)
The left-hand side of the equation is \( \sec \theta \cdot \cot \theta \).

### Step 2: Substitute the definitions of secant and cotangent
We know that:
- \( \sec \theta = \frac{1}{\cos \theta} \)
- \( \cot \theta = \frac{\cos \theta}{\sin \theta} \)

Substituting these definitions into the LHS gives us:
\[ \sec \theta \cdot \cot \theta = \left(\frac{1}{\cos \theta}\right) \cdot \left(\frac{\cos \theta}{\sin \theta}\right) \]

### Step 3: Simplify the expression
Now, we can simplify the expression:
\[ \sec \theta \cdot \cot \theta = \frac{1 \cdot \cos \theta}{\cos \theta \cdot \sin \theta} = \frac{1}{\sin \theta} \]

### Step 4: Recognize the definition of cosecant
We know that:
\[ \csc \theta = \frac{1}{\sin \theta} \]

### Step 5: Compare LHS and RHS
Now we can compare the simplified LHS with the right-hand side (RHS):
\[ \frac{1}{\sin \theta} = \csc \theta \]

### Conclusion
Since both sides are equal, we conclude that:
\[ \sec \theta \cdot \cot \theta = \csc \theta \]
Thus, the statement is **true**.