Which of the following is not defined ?

Options

A. `sin 90^(@)`
B. ` tan 0^(@)`
C. `cos 90^(@)`
D. ` cosec 0^(@)`

Answer

To determine which of the following trigonometric ratios is not defined, we will analyze each option step by step.

### Step-by-Step Solution:

1. **Identify the Trigonometric Ratios**: We need to check the values of the following trigonometric ratios:
- sin 90°
- tan 0°
- cos 90°
- cosec 0°

2. **Calculate sin 90°**:
- The value of sin 90° is 1.
- Since 1 is a defined value, this option is defined.

3. **Calculate tan 0°**:
- The value of tan 0° can be calculated as:
\[ \tan 0° = \frac{\sin 0°}{\cos 0°} \]
- We know that sin 0° = 0 and cos 0° = 1, thus:
\[ \tan 0° = \frac{0}{1} = 0 \]
- Since 0 is a defined value, this option is defined.

4. **Calculate cos 90°**:
- The value of cos 90° is 0.
- Since 0 is a defined value, this option is defined.

5. **Calculate cosec 0°**:
- The value of cosec 0° can be calculated as:
\[ \csc 0° = \frac{1}{\sin 0°} \]
- We know that sin 0° = 0, thus:
\[ \csc 0° = \frac{1}{0} \]
- The expression \(\frac{1}{0}\) is not defined in mathematics.

6. **Conclusion**:
- Among the options, cosec 0° is the only one that is not defined.

### Final Answer:
The trigonometric ratio that is not defined is **cosec 0°**.

---