Question

Cos2 x - cos x - 2 = 0​

Answer 1

Ответ:

..............

Объяснение:

както так

Answer 2

To solve the equation $\cos(2x) - \cos(x) - 2 = 0$, you can use a trigonometric identity to simplify it.

First, let's rewrite $\cos(2x)$ using the double-angle identity for cosine:

$\cos(2x) = 2\cos^2(x) - 1$

Now, replace $\cos(2x)$ in the equation:

$2\cos^2(x) - 1 - \cos(x) - 2 = 0$

Combine like terms:

$2\cos^2(x) - \cos(x) - 3 = 0$

Now, you have a quadratic equation in terms of $\cos(x)$. You can solve it using the quadratic formula:

$\cos(x) = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

In this case, $a = 2$, $b = -1$, and $c = -3$. Plug these values into the quadratic formula:

$\cos(x) = \frac{-(-1) \pm \sqrt{(-1)^2 - 4(2)(-3)}}{2(2)}$

Simplify:

$\cos(x) = \frac{1 \pm \sqrt{1 + 24}}{4}$

$\cos(x) = \frac{1 \pm \sqrt{25}}{4}$

$\cos(x) = \frac{1 \pm 5}{4}$

Now, you have two possible solutions for $\cos(x)$:

1. $\cos(x) = \frac{1 + 5}{4} = \frac{6}{4} = \frac{3}{2}$

2. $\cos(x) = \frac{1 - 5}{4} = \frac{-4}{4} = -1$

However, the cosine function only takes values between -1 and 1, so the second solution, $\cos(x) = -1$, is valid.

So, the solution to the equation $\cos(2x) - \cos(x) - 2 = 0$ is:

$\cos(x) = -1$

Now, you can find the values of $x$ that satisfy this equation. Since $\cos(x) = -1$ when $x = \pi$ (plus any integer multiple of $2\pi$), the solutions are:

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