Question

2√ 2cos^2x = 1 + √ 2(2 корней из 2 * косинус квадрат х = 1 + корень из 2)Помогите пожалуйста решить тригонометрическое уравнение, только поподробней, не пропуская шагов :) Спасибо

Answer 1

Стремное оно, ну да ладно, наверное так:

2√2*cos²x=1+√2;

cos²x=(1+√2/2√2);

cosx=√(1/2√2+1/2);

x=±arccos√(1/2√2+1/2)+2πn. n∈Z.

Answer 2

Solving the Trigonometric Equation

To solve the trigonometric equation 2√(2cos^2x) = 1 + √(2(2+√2)cos^2x) = 1 + √2, we can follow these steps:

1. Isolate the Trigonometric Function First, let's isolate the trigonometric function by moving all terms to one side of the equation.

2√(2cos^2x) - √(2(2+√2)cos^2x) - 1 = 0

2. Substitute for cos^2x We can substitute u = cos^2x to simplify the equation.

2√(2u) - √(2(2+√2)u) - 1 = 0

3. Solve for u Now, we can solve for u using the quadratic formula.

u = (-b ± √(b^2 - 4ac)) / (2a)

where a = 2, b = -√(2(2+√2)), and c = -1.

After solving for u, we can substitute back cos^2x and solve for x.

Let's proceed with these steps to find the solution.