https://file.aiquickdraw.com/mathbot/file/1725453550664sfhv3kag.jpg

The image provided shows a display with an exercise labeled as "Exercise 6". The content on the screen includes a list of mathematical problems, although the text is a bit unclear. Let me extract the text and interpret the mathematical content for you.

---

### Exercise 6:

1. **Prove**: \( \sin(x) + \cos(x) = \sqrt{2} \sin\left(x + \frac{\pi}{4}\right) \)

2. Solve for \( x \):

   a. \( \tan(2x) = 3 \)

   b. \( \cos(2x) = -1 \)

3. If \( \sin(x) = 0.6 \) and \( 0 \leq x \leq \frac{\pi}{2} \), find \( \cos(2x) \).

---

Let me know if you need help with solving these problems or further explanation! Here are some questions that can guide you deeper into this topic:

1. How do you simplify trigonometric identities to prove the given equation?
2. What are the steps to solve a trigonometric equation like \( \tan(2x) = 3 \)?
3. How can you find the value of \( x \) given a trigonometric function within a specific interval?
4. What is the significance of double-angle identities in solving trigonometric equations?
5. How do you determine the values of other trigonometric functions when one function value is given?

**Tip:** When working with trigonometric equations, always consider using identities to simplify the expressions. This can often lead to easier solutions or even direct proofs.

The original question submitted by the user as text is unclear due to the blurry text in the image provided. However, it appears to be related to trigonometric identities and equations.

Solve trigonometric identities and equations with Exercise 6. This problem covers key trigonometric concepts, including the Pythagorean identity and double-angle formulas. Suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation