Question

1+cos2x = cos x /////////////

Answer 1

Ответ:

Объяснение:

1+cos2x = cos x

cos2x=cos²x - sin²x  .   1= sin² x + cos² x

1 +cos²x -  sin²x - cos x =0

sin² x + cos² x   + cos² x -sin² x - cos x=0

2 cos² X - cos X=  0

2 cos X( cos X - 1) =0

2 cos X=0      или   ( cos X - 1) =0

Х=п/2+пк                   cos X = 1

                                    Х= пк

Сводим оба ответа в один и получаем ответ

Х=  п/2 *к все точки единичного круга на осях координат

Answer 2

To solve the equation $1 + \cos(2x) = \cos(x)$, we'll first simplify and then solve for $x$:

Let's use the double-angle identity for cosine: $\cos(2x) = 2\cos^2(x) - 1$. Substituting this into the equation, we get:

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

Now, let's rearrange the equation:

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

Divide both sides by $\cos(x)$:

$2\cos(x) = 1$

Now, isolate $\cos(x)$:

$\cos(x) = \frac{1}{2}$

To find the values of $x$ that satisfy this equation, we can look at the unit circle or use inverse cosine (arccosine). The solutions for $x$ are:

$x = \frac{\pi}{3} + 2n\pi$ $x = \frac{5\pi}{3} + 2n\pi$

where $n$ is an integer. These solutions represent the periodicity of the trigonometric functions.