Question

Cos ( pi\6 + x) = -1

Answer 1

Так как cosx=-1                                                                                                      x=pi + 2pi*k                                                                                                           pi /6 +x= pi +2pi*k  
x= pi - pi /6+2 pi*k
x=5*pi/6+2pi*k

Answer 2

To find the value of $x$ that satisfies the equation $\cos(\pi/6 + x) = -1$, we need to determine the angle whose cosine is -1.

The cosine function has a period of $2\pi$, which means that for any angle $t$, $\cos(t) = \cos(t + 2\pi)$. Additionally, the cosine function is an even function, so $\cos(t) = \cos(-t)$.

We know that $\cos(\pi) = -1$, so we can rewrite the equation as follows:

$\pi/6 + x = \pi + 2n\pi$, where $n$ is an integer.

Subtracting $\pi/6$ from both sides:

$x = \pi + 2n\pi - \pi/6$

Simplifying:

$x = 5\pi/6 + 2n\pi$

So the solution for $x$ is $x = 5\pi/6 + 2n\pi$, where $n$ can be any integer.