Which of the following is not correct ?

Options

A. `cos(cos 1) gt cos(sin 1)`
B. `sin(cos 1) lt sin(sin 1)`
C. `cos(cos 2) gt sin (cos 2)`
D. none of these

Explanation

To solve the problem of determining which of the following options is not correct, we will analyze each option step by step.

### Step 1: Understand the Trigonometric Values
We know that:
- For angles less than \( \frac{\pi}{4} \) (or 45 degrees), \( \cos(x) > \sin(x) \).
- For angles greater than \( \frac{\pi}{4} \), \( \sin(x) > \cos(x) \).
- The values of \( \sin(x) \) and \( \cos(x) \) range between 0 and 1.

### Step 2: Analyze Each Option
Let's denote the options as follows:
1. \( \cos(\cos(1)) > \sin(\sin(1)) \)
2. \( \sin(\cos(1)) < \sin(\sin(1)) \)
3. \( \cos(\cos(2)) > \sin(\cos(2)) \)
4. None of these

**Option 1: \( \cos(\cos(1)) > \sin(\sin(1)) \)**
- Since \( 1 \) radian is greater than \( \frac{\pi}{4} \), we know \( \cos(1) < \sin(1) \).
- Therefore, \( \cos(\cos(1)) < \cos(1) \) and \( \sin(\sin(1)) > \sin(1) \).
- Thus, \( \cos(\cos(1)) < \sin(\sin(1)) \) is likely true.

**Option 2: \( \sin(\cos(1)) < \sin(\sin(1)) \)**
- Since \( \cos(1) < \frac{\pi}{4} \), we have \( \sin(\cos(1)) > \sin(\sin(1)) \).
- Therefore, this option is incorrect.

**Option 3: \( \cos(\cos(2)) > \sin(\cos(2)) \)**
- Since \( 2 \) radians is also greater than \( \frac{\pi}{4} \), we have \( \cos(2) < \sin(2) \).
- Thus, \( \cos(\cos(2)) < \sin(\cos(2)) \), making this option also incorrect.

### Step 3: Conclusion
From our analysis:
- Option 1 is correct.
- Option 2 is incorrect.
- Option 3 is also incorrect.

Thus, the answer to the question "Which of the following is not correct?" is **Option 2**.