Which of the following incorrect?

Options

A. `cos 90^@ =0`
B. `sin^2 theta - cos^2 theta = 1`
C. `sec^2 theta-tan^2 theta = 1`
D. `cosec^2 theta - cot^2 theta = 1`

Answer

To solve the question "Which of the following is incorrect?", we need to evaluate each of the given options based on trigonometric identities.

### Step-by-Step Solution:

1. **Evaluate Option 1: cos 90° = 0**
- We know from trigonometric values that cos 90° is indeed 0.
- **Conclusion**: This statement is correct.

2. **Evaluate Option 2: sin²θ - cos²θ = 1**
- We recall the Pythagorean identity: sin²θ + cos²θ = 1.
- The statement given is sin²θ - cos²θ = 1, which is not correct.
- **Conclusion**: This statement is incorrect.

3. **Evaluate Option 3: 1 + sin²θ = sec²θ**
- The correct identity is: 1 + tan²θ = sec²θ, not involving sin²θ.
- Therefore, this statement is also incorrect.
- **Conclusion**: This statement is incorrect.

4. **Evaluate Option 4: 1 + cot²θ = cosec²θ**
- This is a well-known trigonometric identity.
- **Conclusion**: This statement is correct.

### Final Answer:
The incorrect options are Option 2 and Option 3. However, since the question asks for which of the following is incorrect, we can conclude that Option 2 is the primary incorrect statement as it directly contradicts the established trigonometric identity.