Question

Sin3x-2cos2x-sinx=0 помогите пожалуйста))

Answer 1

Sin3x-2cos2x-sinx=0
(sin3x-sinx)-2cos2x=-
2sinxcos2x-2cos2x=0
2cos2x(sinx-1)=0
cos2x=0                  sinx-1=0
2x=π/2+πn,n∈Z      sinx=1
x=π/4+πn/2, n∈Z      x=π/2+2πk, k∈Z

Answer 2

Solving the Equation Sin(3x) - 2cos(2x) - sin(x) = 0

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

Step 1: Simplify the Equation

To simplify the equation, we can use the following trigonometric identities:

- Sin(3x) = 3Sin(x) - 4Sin^3(x) (triple angle identity for sine) - Cos(2x) = 1 - 2Sin^2(x) (double angle identity for cosine)

Substituting these identities into the equation, we get:

3Sin(x) - 4Sin^3(x) - 2(1 - 2Sin^2(x)) - Sin(x) = 0

Simplifying further, we have:

-4Sin^3(x) + 5Sin(x) - 2 = 0

Step 2: Solve the Cubic Equation

The equation -4Sin^3(x) + 5Sin(x) - 2 = 0 is a cubic equation in terms of Sin(x). To solve this equation, we can use numerical methods or approximation techniques. However, there is no exact algebraic solution for this equation.

Step 3: Approximate Solutions

Using numerical methods or approximation techniques, we can find approximate solutions for the equation. One way to do this is by using a graphing calculator or software that can plot the equation and find its roots.

Based on the available search results, I couldn't find the exact solutions for this equation. However, if you have specific values or constraints for x, I can help you find approximate solutions or discuss the properties of the equation further.

Please let me know if there's anything else I can assist you with!