Question

Cos 10x = cos квадрат х - sin квадрат х

Answer 1

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Answer 2

The equation you provided is:

cos(10x) = cos^2(x) - sin^2(x)

Using a trigonometric identity, we know that cos^2(x) - sin^2(x) is equal to cos(2x). Therefore, we can rewrite the equation as:

cos(10x) = cos(2x)

Now, we can solve for x. To do that, we'll use the fact that the cosine function is periodic with a period of 2π. This means that for any angle x, cos(x + 2π) = cos(x).

Since cos(10x) = cos(2x), we can write:

10x = 2x + 2πn

where n is an integer representing the number of full periods the angles x and 2x have shifted by.

Simplifying the equation:

10x - 2x = 2πn

8x = 2πn

Dividing both sides by 8:

x = (2πn) / 8

x = πn / 4

Therefore, the general solution for x is:

x = πn / 4

where n is an integer.