Question

Решите уравнения 3sin^2x-4sinxcosx+cos^2x=0 Помогите пожалуйста

Answer 1

Ответ: Π/4+Πk, k€Z; arctg1/3+Πm, m€Z

Answer 2

Solving the Trigonometric Equation

To solve the equation 3sin^2x - 4sinxcosx + cos^2x = 0, we can use the trigonometric identity sin^2x + cos^2x = 1 to simplify the equation and then solve for the variable.

First, let's use the identity sin^2x + cos^2x = 1 to simplify the given equation: 3sin^2x - 4sinxcosx + cos^2x = 0 3(1 - cos^2x) - 4sinxcosx + cos^2x = 0 3 - 3cos^2x - 4sinxcosx + cos^2x = 0 3 - 2cos^2x - 4sinxcosx = 0

Now, we have the equation 3 - 2cos^2x - 4sinxcosx = 0. We can solve for x using trigonometric identities and equations.

Let's proceed with solving the equation.