Giá trị biểu thức A

I'm happy to help with your math questions! Let's go through the problems you've mentioned.

### Câu 17:
Given \( \tan a = 2 \), we need to find the value of \( A = \frac{\sin^2 a + 3 \sin a \cos a + 2 \cos^2 a}{3 \sin^2 a + 4 \cos^2 a} \).

Using \( \ tan a = \frac{\sin a}{\cos a} \),
\[
\sin a = \frac{2\cos a}{\sqrt{5}} \quad \text{and} \quad \cos a = \frac{\cos a}{\sqrt{5}}
\]

Substituting back into \( A \) and simplifying will yield the answer.

### Câu 18:
To find the minimum and maximum of \( y = 3 - 2\sin x \):
- The maximum occurs when \( \sin x = -1 \): \( y_{\text{max}} = 3 - 2(-1) = 5 \)
- The minimum occurs when \( \sin x = 1 \): \( y_{\text{min}} = 3 - 2(1) = 1 \)

So, \( \text{min } y = 1 \); \( \text{max } y = 5 \) (answer B).

### Câu 19:
For \( y = \cos^2 x - \cos x + 2 \),
- This is a quadratic function in terms of \( u = \cos x \) which can be minimized.
- The minimum would occur at the vertex of the quadratic. Solving gives minimum value and maximum value (calculate accordingly).

### Câu 20:
The false statement can be checked based on the behavior of the functions mentioned, especially over the given intervals.

### Câu 21:
Identifying odd and even functions:
- \( y = \sin x \) and \( y = \cos x \) are indeed odd functions.
- \( y = \tan x \) is also an odd function.

### Câu 22:
The period of \( y = \sin^4 x \) can be determined by finding the base period and adjusting for \( k \).

### Câu 23:
Using \( y = \cos^2 \left( \frac{x}{3} \right) \), identify the period which depends on the transformation from \( \cos x \).

### Câu 24:
The general solution for \( \cot x = 1 \) is \( x = \frac{\pi}{4} + k\pi, k \in \mathbb{Z} \).

### Câu 25:
For \( \tan 2x = 1 \), the general solution can be determined.

### Câu 26:
Identify values when \( \cos x = -\frac{1}{2} \); use fundamental angles.

### Câu 27:
Solving \( \sin (2x - \frac{\pi}{4}) = \sin \frac{3\pi}{4} \) using properties of sine.

### Câu 28:
To solve \( \tan 3x \cdot \cot 2x = 1 \), restructure into workable forms for solutions.

### Câu 29:
Typically, \( 2 \cos 5x + 1 = 0 \) can be solved for values of \( x \) interval-wise.

If you can provide specific areas where you have doubts, I can assist further!