Question

(cosx-1)*(tgx+корень из 3)*корень из cosx =0

Answer 1

1) cosx-1=0
cosx=1
x=2pi*n
2)tgx+корень из 3=0
tgx= - корень из 3
x=-pi/3+pi*k
3)корень из cosx=0
cosx=0
x=pi/2+pi*m

Answer 2

To solve the equation $(\cos(x)-1)(\tan(x)+\sqrt{3})\sqrt{\cos(x)} = 0$, we need to find the values of $x$ that satisfy the equation. To do that, we'll set each factor equal to zero and solve for $x$:

1. $\cos(x) - 1 = 0$: Adding 1 to both sides, we get $\cos(x) = 1$. The solutions to this equation are $x = 2n\pi$, where $n$ is an integer.

2. $\tan(x) + \sqrt{3} = 0$: Subtracting $\sqrt{3}$ from both sides, we get $\tan(x) = -\sqrt{3}$. The solutions to this equation are $x = \frac{2n\pi}{3}$, where $n$ is an integer.

3. $\sqrt{\cos(x)} = 0$: To have a real solution for $x$, $\cos(x)$ must be non-negative, so $\cos(x) \geq 0$. Since $\cos(x)$ can't be negative, this equation doesn't provide any additional solutions.

Now, we need to find the common solutions among the solutions obtained from the three equations above. So, let's find the intersection:

The solutions from the first equation are $x = 2n\pi$. The solutions from the second equation are $x = \frac{2n\pi}{3}$.

To find the common solutions, we need to find the values of $n$ that satisfy both equations. The solutions that satisfy both equations are the multiples of $\frac{2\pi}{3}$:

$x = \frac{2n\pi}{3}$, where $n$ is an integer.

These are the solutions to the given equation $(\cos(x)-1)(\tan(x)+\sqrt{3})\sqrt{\cos(x)} = 0$.