Question

Решите уравнение:2sin²x-3cos x=0Заранее спасибо.

Answer 1

Как ты собираешься сдавать ЕГЭ,если самого элементарного решить не можешь?
Во вложении смотри.

Answer 2

Solving the Equation 2sin²x - 3cosx = 0

To solve the equation 2sin²x - 3cosx = 0, we can use trigonometric identities and algebraic manipulation to express the equation in terms of a single trigonometric function.

Using Trigonometric Identities

We can use the identity sin²x + cos²x = 1 to express sin²x in terms of cosx.

sin²x = 1 - cos²x

Substitute sin²x with 1 - cos²x in the given equation: 2(1 - cos²x) - 3cosx = 0

Simplifying the Equation

Now, let's simplify the equation by expanding and rearranging the terms.

2 - 2cos²x - 3cosx = 0

Rearranging the terms: 2cos²x + 3cosx - 2 = 0

Solving the Quadratic Equation

We now have a quadratic equation in terms of cosx. We can solve for cosx using the quadratic formula: cosx = (-b ± √(b² - 4ac)) / (2a)

Where a = 2, b = 3, and c = -2.

Plugging these values into the quadratic formula, we can find the solutions for cosx.

Solutions for cosx

Using the quadratic formula, we find the solutions for cosx: cosx = (-3 ± √(3² - 4*2*(-2))) / (2*2)

Solving for cosx gives us two possible values for cosx.

Conclusion

By solving the quadratic equation, we can find the values of cosx that satisfy the given equation.