Question

Sin2xcos3x = 0 (решите уравнение)

Answer 1

Каждый множитель приравниваем к 0.Затем применяем формулы частных случаев.

Answer 2

sin2xcos3c=0
sin2x=0⇒2x=πn⇒x=πn/2
cos3x=0⇒3x=π/2+πn⇒x=π/6+πn/3

Answer 3

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

To solve the equation sin(2x)cos(3x) = 0, we need to find the values of x that satisfy this equation.

The equation sin(2x)cos(3x) = 0 can be solved by finding the values of x for which either sin(2x) or cos(3x) is equal to 0.

Using Trigonometric Identities: We can use the trigonometric identity sin(2x) = 2sin(x)cos(x) and cos(3x) = 4cos^3(x) - 3cos(x) to simplify the equation and find the solutions for x.

Solving sin(2x) = 0: The solutions for sin(2x) = 0 can be found by solving for x in the equation sin(2x) = 0.

Solving cos(3x) = 0: The solutions for cos(3x) = 0 can be found by solving for x in the equation cos(3x) = 0.

Solutions:

The solutions for the equation sin(2x)cos(3x) = 0 are the values of x that satisfy either sin(2x) = 0 or cos(3x) = 0.

Solutions for sin(2x) = 0: The solutions for sin(2x) = 0 are x = kπ, where k is an integer.

Solutions for cos(3x) = 0: The solutions for cos(3x) = 0 are x = (2k + 1)π/6, where k is an integer.

Therefore, the solutions for the equation sin(2x)cos(3x) = 0 are x = kπ for sin(2x) = 0 and x = (2k + 1)π/6 for cos(3x) = 0.

I hope this helps! If you have any further questions, feel free to ask.