Which of the following is incorrect

Options

A. `sin theta = (1)/(5)`
B. ` cos theta = 1 `
C. ` sec theta = (1)/(2)`
D. `tan theta = 20 `

Answer

To determine which of the given options is incorrect, we will analyze each option based on the properties of trigonometric functions.

### Step-by-Step Solution:

1. **Analyze the first option: sin θ = 1/5**
- The sine function, sin θ, has a range of values between -1 and 1 (inclusive).
- Since 1/5 is equal to 0.2, which lies between -1 and 1, this option is valid.
- **Conclusion:** This option is correct.

2. **Analyze the second option: cos θ = 1**
- The cosine function, cos θ, also has a range of values between -1 and 1 (inclusive).
- The value of 1 is within this range, so this option is valid.
- **Conclusion:** This option is correct.

3. **Analyze the third option: sin θ = 1/2**
- The equation sin θ = 1/2 implies that θ can take specific values (like 30° or 150°).
- However, the statement given in the transcript suggests a misunderstanding: it states that sin θ = 1/cos θ, leading to cos θ = 2.
- The cosine function cannot equal 2, as its range is also between -1 and 1.
- **Conclusion:** This option is incorrect.

4. **Analyze the fourth option: tan θ = 20**
- The tangent function, tan θ, can take any real number value from -∞ to +∞.
- Therefore, tan θ = 20 is valid.
- **Conclusion:** This option is correct.

### Final Conclusion:
The incorrect option is the third one: **sin θ = 1/2**, because it leads to an impossible value for cos θ.

---