Question

Найдите решение уравнения принадлежащему отрезку cos2x+cosx=0 ; [0; п]

Answer 1

Cos(2x)+cosx=0   [0;π]
cos²x-sin²x+cosx=0
cos²x-(1-cos²x)+cosx=0
cos²x-1+cos²x+cosx=0
2cos²x+cosx-1=0
cosx=t
2t²+t-1=0    D=9
t₁=-1     cosx=-1       x₁=π
t₂=1/2   cosx=1/2      x₂=π/3
Ответ: x₁=π     x₂=π/3.

Answer 2

Solution for the Equation on the Interval [0, π]

To find the solution to the equation cos(2x) * cos(x) = 0 on the interval [0, π], we can use the following steps:

1. Identify the Values of x for which cos(2x) = 0 or cos(x) = 0: - The equation can be solved by finding the values of x for which either cos(2x) = 0 or cos(x) = 0 [[3]](https://postypashki.ru/wp-content/uploads/2020/09/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0_%D0%9F%D0%BE%D1%81%D0%BE%D0%B1%D0%B8%D0%B5_%D0%B4%D0%BB%D1%8F_%D0%BF%D0%BE%D1%81%D1%82%D1%83%D0%BF%D0%B0%D1%8E%D1%89%D0%B8%D1%85_%D0%B2_%D0%B2%D1%83%D0%B7%D1%8B_%D0%A8%D0%B0%D0%B1%D1%83%D0%BD%D0%B8%D0%BD.pdf).

2. Solving for cos(2x) = 0: - The solutions for cos(2x) = 0 can be found by solving the equation cos(2x) = 0, which gives us the values of x for which cos(2x) equals 0 [[3]](https://postypashki.ru/wp-content/uploads/2020/09/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0_%D0%9F%D0%BE%D1%81%D0%BE%D0%B1%D0%B8%D0%B5_%D0%B4%D0%BB%D1%8F_%D0%BF%D0%BE%D1%81%D1%82%D1%83%D0%BF%D0%B0%D1%8E%D1%89%D0%B8%D1%85_%D0%B2_%D0%B2%D1%83%D0%B7%D1%8B_%D0%A8%D0%B0%D0%B1%D1%83%D0%BD%D0%B8%D0%BD.pdf).

3. Solving for cos(x) = 0: - Similarly, the solutions for cos(x) = 0 can be obtained by solving the equation cos(x) = 0, which provides the values of x for which cos(x) equals 0 [[3]](https://postypashki.ru/wp-content/uploads/2020/09/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0_%D0%9F%D0%BE%D1%81%D0%BE%D0%B1%D0%B8%D0%B5_%D0%B4%D0%BB%D1%8F_%D0%BF%D0%BE%D1%81%D1%82%D1%83%D0%BF%D0%B0%D1%8E%D1%89%D0%B8%D1%85_%D0%B2_%D0%B2%D1%83%D0%B7%D1%8B_%D0%A8%D0%B0%D0%B1%D1%83%D0%BD%D0%B8%D0%BD.pdf).

4. Combining the Solutions: - By combining the solutions obtained from steps 2 and 3, we can determine the values of x that satisfy the original equation on the interval [0, π].

Conclusion

By following the steps outlined above, the solutions for the equation cos(2x) * cos(x) = 0 on the interval [0, π] can be determined.