Question

Sin2x+√3cos2x=2cos3x​

Answer 1

Ответ:

если это график, то вот

Объяснение:

надеюсь, что это верно

Answer 2

To solve the equation sin(2x) + √3cos(2x) = 2cos(3x), we can use trigonometric identities and algebraic manipulations. Let's break it down step by step:

1. Start with the trigonometric identity for cos(2x): cos(2x) = 1 - 2sin²(x)

   Now, substitute this identity into the equation: sin(2x) + √3(1 - 2sin²(x)) = 2cos(3x)

2. Expand the equation using the distributive property: sin(2x) + √3 - 2√3sin²(x) = 2cos(3x)

3. Rearrange the terms to group the sin²(x) term: -2√3sin²(x) + sin(2x) = 2cos(3x) - √3

4. Use the double-angle identity for sin(2x): sin(2x) = 2sin(x)cos(x)

   Now, substitute this identity into the equation: -2√3sin²(x) + 2sin(x)cos(x) = 2cos(3x) - √3

5. Factor out sin(x) from the left side: sin(x)(-2√3sin(x) + 2cos(x)) = 2cos(3x) - √3

6. Recall the Pythagorean identity: sin²(x) + cos²(x) = 1 Rearrange it to get cos²(x) = 1 - sin²(x)

   Substitute this identity into the factor: sin(x)(-2√3sin(x) + 2√(1 - sin²(x))) = 2cos(3x) - √3

7. Distribute the sin(x) through the factor: -2√3sin²(x) + 2√(1 - sin²(x)))sin(x) = 2cos(3x) - √3

8. Simplify the equation further: -2√3sin³(x) + 2√(1 - sin²(x)))sin(x) = 2cos(3x) - √3

9. Apply the triple-angle identity for sin(3x): sin(3x) = 3sin(x) - 4sin³(x)

   Substitute this identity into the equation: -2√3sin³(x) + 2√(1 - sin²(x)))sin(x) = 2cos(3x) - √3 -2√3sin³(x) + 2√(1 - sin²(x)))sin(x) = 2cos(3x) - √3(3sin(x) - 4sin³(x))

10. Distribute the terms on the right side: -2√3sin³(x) + 2√(1 - sin²(x)))sin(x) = 2cos(3x) - 3√3sin(x) + 4√3sin³(x)

11. Simplify the equation further: -2√3sin³(x) + 2√(1 - sin²(x)))sin(x) = 2cos(3x) - 3√3sin(x) + 4√3sin³(x)

12. Combine like terms: -2√3sin³(x) + 2√(1 - sin²(x)))sin(x) - 4√3sin³(x) + 3√3sin(x) = 2cos(3x)

13. Rearrange the terms: (-2√3sin³(x) - 4√3sin³(x)) + (2√(1 - sin²(x)))sin(x) + 3√3sin(x) = 2cos(3x)

14. Combine like terms: -6√3sin³(x) + (2√(1 - sin²(x)))sin(x) + 3√3sin(x) = 2cos(3x)

Now, the equation is in terms of sin(x) and cos(3x). Solving it further might involve using additional trigonometric identities or numerical methods. If you have specific values or a range for x, please provide them to obtain a more specific solution.