Question

Помогите решить 1)Решите уравнение 2) Найдите все корни этого уравнения, принадлежащие промежутку

Answer 1

  $cos2x=2cos^2x-1\; \; \; (formyla)\\\\4\cdot (2sinx\cdot cosx)\cdot cos^2x-2sin2x-(2cos^2x-1)=0\\\\4sin2x\cdot cos^2x-2sin2x-cos2x=0\\\\2sin2x(2cos^2x-1)-cos2x=0\\\\2sin2x\cdot cos2x-cos2x=0\\\\cos2x(2sin2x-1)=0\\\\a)cos2x=0,\; 2x=\frac{\pi }{2}+\pi n,\; n\in Z\\\\x=\frac{\pi}{4}+\frac{\pi n}{2}$
$b)2sin2x-1=0,\; \; sin2x=\frac{1}{2},\; 2x=(-1)^k\cdot \frac{\pi}{6}+\pi k,\; k\in Z\\\\x=(-1)^k\frac{\pi}{12}+\frac{\pi k}{2}$
Интервалу $[-\frac{3\pi }{2},-2\pi ]$ принадлежат углы $-\frac{\pi}{4}\; (n=-4),-\frac{19\pi}{12}\; (k=-3)$

Answer 2

Solving the Equation

To solve the equation and find all the roots belonging to the interval, we need to consider the provided equation and the interval.

The equation and interval are not explicitly mentioned in the query. However, based on the available search results, I'll provide a general approach to solving equations and finding roots within a given interval.

Equation and Interval

The specific equation and interval are not provided in the query. To provide a more accurate solution, please specify the equation and the interval for which you need to find the roots.

General Approach

To solve an equation and find its roots within a given interval, the following general approach can be used:

1. Solving the Equation: - Identify the given equation, for example, \(f(x) = 0\). - Use algebraic methods or trigonometric identities to simplify the equation and express it in a form where the roots can be easily determined.

2. Finding Roots within the Interval: - Once the equation is simplified, use methods such as factoring, the quadratic formula, or trigonometric identities to find the roots of the equation. - To find the roots within a specific interval, substitute the values from the interval into the equation and check for solutions within that range.

Conclusion

To provide a more specific and accurate solution, please provide the equation and the interval for which you need to find the roots. This will enable me to offer a tailored and precise approach to solving the equation and finding the roots within the specified interval.