Incorrect statement is

Options

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

Answer

To determine which statement is incorrect among the given options, we will analyze each option step by step.

### Step-by-Step Solution:

1. **Check Option 1: \( \sin \theta = -\frac{1}{5} \)**
- The sine function, \( \sin \theta \), has a range of values between -1 and 1, inclusive.
- Since \( -\frac{1}{5} \) lies within this range, this statement is **correct**.

2. **Check Option 2: \( \cos \theta = 1 \)**
- The cosine function, \( \cos \theta \), also has a range of values between -1 and 1, inclusive.
- Since \( 1 \) is within this range, this statement is **correct**.

3. **Check Option 3: \( \sec \theta = \frac{1}{2} \)**
- The secant function is defined as \( \sec \theta = \frac{1}{\cos \theta} \).
- If \( \sec \theta = \frac{1}{2} \), then \( \cos \theta = \frac{1}{\sec \theta} = \frac{1}{\frac{1}{2}} = 2 \).
- The cosine function cannot take a value greater than 1. Therefore, this statement is **incorrect**.

4. **Check Option 4: \( \tan \theta = 20^\circ \)**
- The tangent function can take any real number value, so this statement is **correct**.

### Conclusion:
After evaluating all the options, we find that the incorrect statement is:

**Option 3: \( \sec \theta = \frac{1}{2} \)**

### Final Answer:
Hence, the answer is **Option 3**.

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