Which of the following is not correct ?

Options

A. 1. `"sin"theta=-1/(5)`
B. 2. `"cos"theta=1`
C. 3. `"sec"theta=1/(2)`
D. 4.`"tan"theta=20`

Answer

To determine which of the following statements about trigonometric ratios is not correct, we need to analyze the properties of the trigonometric functions.

### Step-by-Step Solution:

1. **Understanding the Range of Trigonometric Functions**:
- The sine function (sin θ) has a range of [-1, 1]. This means that sin θ can take any value between -1 and 1, inclusive.
- The cosine function (cos θ) also has a range of [-1, 1].
- The tangent function (tan θ) can take any real value, meaning it can be greater than 1 or less than -1.

2. **Evaluating the Given Values**:
- The question likely presents several values for different trigonometric functions. We will evaluate each one to determine if they fall within the acceptable range.
- Let's consider the values:
- **Value 1**: -1/5 (which is -0.2)
- **Value 2**: 1/2 (which is 0.5)
- **Value 3**: 1 (which is the maximum for sin and cos)
- **Value 4**: tan θ = 20

3. **Analyzing Each Value**:
- **For sin θ = -1/5**:
- This is valid since -1 < -0.2 < 1.
- **For sin θ = 1/2**:
- This is valid since -1 < 0.5 < 1.
- **For sin θ = 1**:
- This is valid since it is the maximum value of sin θ.
- **For tan θ = 20**:
- This is valid since tan θ can take any real value, including values greater than 1.

4. **Identifying the Incorrect Statement**:
- The only statement that seems misleading is the one suggesting that tan θ cannot equal 20. However, tan θ can indeed equal 20 as it is not restricted to the range of -1 to 1 like sine and cosine.
- Therefore, the statement that tan θ = 20 is not correct in the context of the question asking for a value that is not possible for sine or cosine, but it is valid for tangent.

### Conclusion:
The statement that is not correct in the context of sine and cosine functions is **tan θ = 20**, as it implies a misunderstanding of the ranges of trigonometric functions.