Question

(cos4x+1)(sin2x-1)=0

Answer 1

Ну тут либо cos4х+1=0, откуда cos 4x=-1 и х=45 гр., либо sin2x-1=0, откуда sin2x=1 и х=22,5 гр.

Answer 2

I can answer your question in detail. The equation (cos4x+1)(sin2x-1)=0 has two factors, so we can use the zero product property to find the solutions. That is, we can set each factor equal to zero and solve for x.

The first factor is cos4x+1=0. To solve for x, we can subtract 1 from both sides and then use the inverse cosine function. We get:

cos4x=-1 4x=cos^-1(-1) 4x=π

To find the general solution, we can add any multiple of 2π to x, since the cosine function is periodic with a period of 2π. So we have:

x=π/4+2πn

where n is any integer.

The second factor is sin2x-1=0. To solve for x, we can add 1 to both sides and then use the inverse sine function. We get:

sin2x=1 2x=sin^-1(1) 2x=π/2

To find the general solution, we can add any multiple of π to x, since the sine function is periodic with a period of π. So we have:

x=π/4+πn

where n is any integer.

To find the complete solution, we can combine the solutions from both factors. We have:

x=π/4+2πn or x=π/4+πn

where n is any integer.

This is the detailed answer to your question. I hope it helps.

If you want to learn more about trigonometric equations, you can check out these web resources:

- [Solve 1+cos4x/1-sin2x=0 | Microsoft Math Solver](https://mathsolver.microsoft.com/en/solve-problem/%60frac%20%7B%201%20%2B%20%60cos%204%20x%20%7D%20%7B%201%20-%20%60sin%202%20x%20%7D%20%3D%200) - [Mathway | Trigonometry Problem Solver](https://www.mathway.com/trigonometry) - [Дано уравнение sin2x ⋅ cos4x=1. А) Решите уравнение. Б) Найдите его ...](https://neznaika.info/q/21677)