Question

Решить уравнение: sinx-sin3x+cos2x=0. Помогите пж.

Answer 1

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

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

Unfortunately, the search results provided by You.com do not contain any relevant information or formulas to directly solve this equation. However, we can still discuss some general strategies to approach this type of equation.

One possible approach is to use trigonometric identities to simplify the equation and then solve for x. Let's try to simplify the equation using some trigonometric identities:

sin(x) - sin(3x) + cos(2x) = 0

We can use the identity sin(a) - sin(b) = 2 * cos((a + b) / 2) * sin((a - b) / 2) to rewrite the equation as:

2 * cos((x + 3x) / 2) * sin((x - 3x) / 2) + cos(2x) = 0

Simplifying further, we get:

2 * cos(2x) * sin(-x) + cos(2x) = 0

Now, let's factor out cos(2x):

cos(2x) * (2 * sin(-x) + 1) = 0

To find the values of x, we need to solve the two equations:

1. cos(2x) = 0 2. 2 * sin(-x) + 1 = 0

For the first equation, cos(2x) = 0, we know that cos(2x) = 0 when 2x = (2n + 1) * (π/2), where n is an integer. Solving for x, we get:

x = (2n + 1) * (π/4)

For the second equation, 2 * sin(-x) + 1 = 0, we can solve for sin(-x):

sin(-x) = -1/2

Using the unit circle or a trigonometric table, we can find that sin(-x) = -1/2 when -x = (7π/6) + 2πn or -x = (11π/6) + 2πn, where n is an integer. Solving for x, we get:

x = -(7π/6) - 2πn or x = -(11π/6) - 2πn

Therefore, the solutions to the equation sin(x) - sin(3x) + cos(2x) = 0 are:

x = (2n + 1) * (π/4) or x = -(7π/6) - 2πn or x = -(11π/6) - 2πn, where n is an integer.

Please note that these are general solutions, and the specific values of x that satisfy the equation may vary depending on the range or constraints given in the problem.

I hope this explanation helps! Let me know if you have any further questions.