Which of the following statement is incorrect

Options

A. `sin theta=-1//5`
B. `cos theta=1`
C. `sec theta=1//2`
D. `tantheta=20`

Answer

To determine which of the given statements is incorrect, let's analyze each statement step by step.

### Step 1: Analyze the first statement
**Statement:** \( \sin \theta = -\frac{1}{5} \)

- The value of \( \sin \theta \) must lie between -1 and 1.
- Since \(-\frac{1}{5} = -0.2\), which is within the range of -1 to 1, this statement is **correct**.

### Step 2: Analyze the second statement
**Statement:** \( \cos \theta = 1 \)

- The value of \( \cos \theta \) must also lie between -1 and 1.
- Since \( 1 \) is within the range of -1 to 1, this statement is **correct**.

### Step 3: Analyze the third statement
**Statement:** \( \sec \theta = \frac{1}{2} \)

- Recall that \( \sec \theta = \frac{1}{\cos \theta} \).
- If \( \sec \theta = \frac{1}{2} \), then \( \cos \theta = 2 \).
- However, the range of \( \cos \theta \) is from -1 to 1. Since \( 2 \) is outside this range, this statement is **incorrect**.

### Step 4: Analyze the fourth statement
**Statement:** \( \tan \theta = 20 \)

- The value of \( \tan \theta \) can take any real number value, ranging from \(-\infty\) to \(+\infty\).
- Since \( 20 \) is within this range, this statement is **correct**.

### Conclusion
The incorrect statement among the options is \( \sec \theta = \frac{1}{2} \) because it leads to \( \cos \theta = 2 \), which is outside the valid range for cosine.