Question

Ctg x/3 = -1/корень из 3

Answer 1

Ответ:

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Пошаговое объяснение:

Answer 2

To solve the equation $\ctg{\frac{x}{3}} = -\frac{1}{\sqrt{3}}$, we first need to find the value of $x$.

Let's manipulate the equation step by step:

1. Start with the given equation: $\ctg{\frac{x}{3}} = -\frac{1}{\sqrt{3}}$.

2. Take the reciprocal of both sides to get $\frac{1}{\ctg{\frac{x}{3}}} = -\sqrt{3}$.

3. Since $\ctg{\theta} = \frac{1}{\tan{\theta}}$, we can rewrite the left side as $\frac{1}{\tan{\frac{x}{3}}} = -\sqrt{3}$.

4. Now, take the reciprocal of both sides again to get $\tan{\frac{x}{3}} = -\frac{1}{\sqrt{3}}$.

5. We know that $\tan{\frac{\pi}{6}} = \frac{1}{\sqrt{3}}$, so $\tan{\frac{x}{3}} = -\tan{\frac{\pi}{6}}$.

6. Using the angle addition formula for tangent, we have $\tan{\left(\frac{x}{3} + \frac{\pi}{6}\right)} = 0$.

7. To find the values of $x$ that satisfy this equation, set $\frac{x}{3} + \frac{\pi}{6} = n\pi$, where $n$ is an integer.

8. Solve for $x$: $x = 3n\pi - \pi$.

Now, $x$ can take any value of the form $3n\pi - \pi$, where $n$ is an integer. So, the general solution for $x$ is $x = 3n\pi - \pi$.