Question

Решить уравнение 7sin^2x-5cos^2x+2=0

Answer 1

7-7cos^2x-5cos^2x+2=0
9-12cos^2x=0
cos^2x=9/12
cos^2x=3/4 (здесь просто дробь сократили на три)
cosx=√3/2
x=+-π/6+2πn: n∈ Z

Answer 2

I can help you solve this equation.

The equation can be simplified by using the trigonometric identity $$\sin^2 x + \cos^2 x = 1$$ and dividing both sides by $$\cos^2 x$$. This gives us $$3\tan^2 x - 1 = 0$$, which can be solved for $$\tan x$$ by taking the square root and adding 1. The solution is $$\tan x = \pm \sqrt{\frac{1}{3}}$$.

To find the values of $$x$$, we need to use the inverse tangent function and add multiples of $$\pi$$ to account for the periodicity of the tangent function. The general solution is $$x = \pm \frac{\pi}{6} + n\pi$$, where $$n$$ is any integer. You can see a detailed explanation of this solution on [this website](https://uchi.ru/otvety/questions/reshit-uravnenie-7sin-2x-5cos-2x-2-0).

I hope this helps you understand how to solve this equation. If you have any other questions, feel free to ask me.