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The image contains the following mathematical problem written in Indonesian:

**Question 2:**
"Himpunan penyelesaian dari persamaan \( \sqrt{3} \cos x + \sin x = 2 \cos 25^\circ \) dengan \( 0^\circ \leq x \leq 360^\circ \)"

Translation:
"Find the solution set of the equation \( \sqrt{3} \cos x + \sin x = 2 \cos 25^\circ \) for \( 0^\circ \leq x \leq 360^\circ \)."

### Steps to Solve:

1. **Understand the equation:**
   \[
   \sqrt{3} \cos x + \sin x = 2 \cos 25^\circ
   \]
   We want to find the values of \( x \) within the interval \( [0^\circ, 360^\circ] \).

2. **Numerical approximation for \( 2 \cos 25^\circ \):**
   Let's first approximate \( 2 \cos 25^\circ \):
   \[
   2 \cos 25^\circ \approx 2 \times 0.9063 = 1.8126
   \]

3. **Substitute this into the equation:**
   \[
   \sqrt{3} \cos x + \sin x = 1.8126
   \]

4. **Use trigonometric identities:**
   To simplify the left-hand side, let's rewrite it in the form of a single trigonometric function. Notice that:
   \[
   \sqrt{3} \cos x + \sin x = 2 \left( \cos \left( x - 30^\circ \right) \right)
   \]
   This uses the identity \( \sqrt{3} \cos x + \sin x \) which matches the standard form \( R \cos(x - \alpha) \).

5. **Solve the simplified equation:**
   We now solve:
   \[
   2 \cos (x - 30^\circ) = 1.8126
   \]
   Dividing both sides by 2:
   \[
   \cos (x - 30^\circ) = 0.9063
   \]

6. **Find general solutions:**
   Using the inverse cosine function:
   \[
   x - 30^\circ = \cos^{-1}(0.9063) = 25^\circ
   \]
   So:
   \[
   x_1 = 25^\circ + 30^\circ = 55^\circ
   \]
   For the second solution, we use \( \cos(\theta) = \cos(360^\circ - \theta) \):
   \[
   x_2 = 360^\circ - 25^\circ + 30^\circ = 365^\circ - 360^\circ = 5^\circ
   \]

7. **Final Solutions:**
   The two solutions within the interval \( [0^\circ, 360^\circ] \) are:
   \[
   x = 55^\circ \quad \text{and} \quad x = 5^\circ
   \]

### Solution Set:
\[
x \in \{ 5^\circ, 55^\circ \}
\]

Would you like any further details or clarifications?

Here are some related questions for deeper understanding:

1. How do you apply the cosine identity to simplify trigonometric equations?
2. What is the geometric interpretation of solving trigonometric equations on the unit circle?
3. Can you explain the process of finding the general solution of trigonometric equations?
4. How does phase shift affect the solutions of trigonometric equations?
5. Why are there typically two solutions for \( \cos x = \text{constant} \) in the interval \( [0^\circ, 360^\circ] \)?

**Tip:** When solving trigonometric equations, always consider the possibility of multiple solutions within the given interval.

Find the solution set of the equation √3 cos(x) + sin(x) = 2 cos(25°) for 0° ≤ x ≤ 360°.

Learn how to solve the trigonometric equation √3 cos(x) + sin(x) = 2 cos(25°) for 0° ≤ x ≤ 360°. This solution involves using trigonometric identities and inverse functions, perfect for students in Grades 10-12.

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