Question

Sin5x-sin3x-2sin4x=0 Помогите, пожалуйста

Answer 1

Ответ:

вообще было. сложно

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Answer 2

Solving the Equation Sin(5x) - Sin(3x) - 2Sin(4x) = 0

To solve the equation Sin(5x) - Sin(3x) - 2Sin(4x) = 0, we can use various trigonometric identities and properties. Let's break it down step by step:

Step 1: Simplify the equation using trigonometric identities. - We can use the identity Sin(A) - Sin(B) = 2Cos((A+B)/2)Sin((A-B)/2) to simplify the equation. - Applying this identity, we get 2Cos(4x)Sin(x) - 2Sin(4x) = 0.

Step 2: Factor out the common term. - We can factor out 2Sin(4x) from the equation: 2Sin(4x)(Cos(x) - 1) = 0.

Step 3: Solve for Sin(4x) = 0. - Setting Sin(4x) = 0, we find that 4x = nπ, where n is an integer. - Solving for x, we get x = nπ/4.

Step 4: Solve for Cos(x) - 1 = 0. - Setting Cos(x) - 1 = 0, we find that Cos(x) = 1. - The only solution for this equation is x = 2πk, where k is an integer.

Therefore, the solutions to the equation Sin(5x) - Sin(3x) - 2Sin(4x) = 0 are x = nπ/4 and x = 2πk, where n and k are integers.

Please note that the above steps are based on the trigonometric identities and properties.