Choose the correct statements among following :
(a) `cos40^(@)gtcos70^(@)`
(b) `sin35^(@)gtsin65^(@)`
(c ) `tan45^(@)lttan46^(@)`
(d) `cot40^(@)ltcot39^(@)`
(e ) `sec20^(@)gtsec40^(@)`
(f) `cosec20^(@)ltcosec30^(@)`

Answer

To solve the question, we will analyze each statement one by one using the properties of trigonometric functions.

### Step-by-Step Solution:

1. **Statement (a): `cos 40° > cos 70°`**
- The cosine function decreases as the angle increases in the range of 0° to 90°. Since 40° is less than 70°, it follows that cos 40° is greater than cos 70°.
- **Conclusion:** True.

2. **Statement (b): `sin 35° > sin 65°`**
- The sine function increases as the angle increases in the range of 0° to 90°. Since 35° is less than 65°, it follows that sin 35° is less than sin 65°.
- **Conclusion:** False.

3. **Statement (c): `tan 45° < tan 46°`**
- The tangent function increases as the angle increases in the range of 0° to 90°. Since 45° is less than 46°, it follows that tan 45° is less than tan 46°.
- **Conclusion:** True.

4. **Statement (d): `cot 40° < cot 39°`**
- The cotangent function decreases as the angle increases in the range of 0° to 90°. Since 40° is greater than 39°, it follows that cot 40° is less than cot 39°.
- **Conclusion:** True.

5. **Statement (e): `sec 20° > sec 40°`**
- The secant function increases as the angle increases in the range of 0° to 90°. Since 20° is less than 40°, it follows that sec 20° is less than sec 40°.
- **Conclusion:** False.

6. **Statement (f): `cosec 20° < cosec 30°`**
- The cosecant function decreases as the angle increases in the range of 0° to 90°. Since 20° is less than 30°, it follows that cosec 20° is greater than cosec 30°.
- **Conclusion:** False.

### Summary of Results:
- Correct Statements: (a), (c), (d)
- Incorrect Statements: (b), (e), (f)

### Final Answer:
The correct statements are (a), (c), and (d).