Question

Cos2x cos12x+sin2xsin12x=-1

Answer 1

Такой вот ответ на данный вопрос

Answer 2

Cos(2x)cos(12x)+sin(2x)sin(12x)=-1
1)cos(-10x)=-1
2)cos(10x)=-1
3)10x=n+2kn,
=x=n/10+kn/5

Answer 3

To prove the equation $\cos(2x) \cos(12x) + \sin(2x) \sin(12x) = -1$, we can use the trigonometric identity:

$\cos(A - B) = \cos A \cos B + \sin A \sin B$

By comparing this identity with the left-hand side of the equation, we can see that $A = 2x$ and $B = 12x$. So, we can rewrite the equation as:

$\cos(2x - 12x) = -1$

Simplifying inside the cosine:

$\cos(-10x) = -1$

Now, we know that the cosine function takes the value of -1 when the argument is an odd multiple of $\pi$:

$-10x = (2n + 1) \pi$

where $n$ is an integer. Solving for $x$:

$x = -\frac{(2n + 1) \pi}{10}$

So, the equation holds true for any integer value of $n$. Thus, the solution to the equation $\cos(2x) \cos(12x) + \sin(2x) \sin(12x) = -1$ is $x = -\frac{(2n + 1) \pi}{10}$, where $n$ is an integer.