Question

Sin3x*ctgx=0 пжжжжжжжжжжжжжжж

Answer 1

Ответ:

sin3x * ctgx = 0

sin3x * (cosx/sinx) =0

sin3x=0 cosx/sinx=0, sinx≠0

3x=pi*n cosx=0

x=(pi*n)/2 x=pi/2 + pi*n

Пошаговое объяснение:

Answer 2

To solve the equation $\sin(3x) \cdot \cot(x) = 0$, we need to find the values of $x$ that satisfy the equation.

The product of two factors is zero when at least one of the factors is zero. Therefore, we have two possibilities:

1. $\sin(3x) = 0$
2. $\cot(x) = 0$

Let's solve each part separately:

Solving $\sin(3x) = 0$:

The sine function is equal to zero when the angle is a multiple of $\pi$. So, we have:

$3x = n\pi$

where $n$ is an integer.

$x = \frac{n\pi}{3}$

Solving $\cot(x) = 0$:

The cotangent function is equal to zero when the cosine function is zero:

$\cot(x) = \frac{\cos(x)}{\sin(x)} = 0$

This occurs when $\cos(x) = 0$. The cosine function is equal to zero when the angle is an odd multiple of $\frac{\pi}{2}$:

$x = (2n + 1)\frac{\pi}{2}$

where $n$ is an integer.

Combine the solutions:

So, the general solutions for the given equation are:

$x = \frac{n\pi}{3} \quad \text{or} \quad x = (2n + 1)\frac{\pi}{2}$

where $n$ is an integer.

These are the values of $x$ that satisfy the equation $\sin(3x) \cdot \cot(x) = 0$.