Find the value of `"cosec"70^(@)-sec20^(@)`

Answer

To find the value of \( \csc 70^\circ - \sec 20^\circ \), we can use the properties of complementary angles in trigonometry.

### Step-by-Step Solution:

1. **Understanding the Definitions**:
- The cosecant function is defined as \( \csc \theta = \frac{1}{\sin \theta} \).
- The secant function is defined as \( \sec \theta = \frac{1}{\cos \theta} \).

2. **Using Complementary Angles**:
- We know that \( \sin(90^\circ - \theta) = \cos \theta \).
- Therefore, \( \csc(90^\circ - \theta) = \sec \theta \).

3. **Applying the Complementary Angle Property**:
- For \( \csc 70^\circ \), we can express it in terms of \( \sec \):
\[ \csc 70^\circ = \sec(90^\circ - 70^\circ) = \sec 20^\circ \]
- This means \( \csc 70^\circ \) is equal to \( \sec 20^\circ \).

4. **Substituting Back into the Expression**:
- Now, we substitute \( \csc 70^\circ \) in the original expression:
\[ \csc 70^\circ - \sec 20^\circ = \sec 20^\circ - \sec 20^\circ \]

5. **Calculating the Final Value**:
- Thus, we have:
\[ \sec 20^\circ - \sec 20^\circ = 0 \]

### Final Answer:
The value of \( \csc 70^\circ - \sec 20^\circ \) is \( 0 \).