Question

Cos^2 (/2x)-sin^2 (2x)=1

Answer 1

Решение задания смотри на фотографии

Answer 2

Let's solve the trigonometric equation:

cos^2(x/2) - sin^2(2x) = 1

To simplify the equation, we'll use some trigonometric identities:

1. cos^2(A) - sin^2(A) = cos(2A)
2. sin(2A) = 2sin(A)cos(A)

Applying these identities to our equation, we get:

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

So, the equation becomes:

cos(x) = 1

To find the solutions, we need to find the values of x that satisfy this equation. In the domain of real numbers, the cosine function has values ranging from -1 to 1.

For cos(x) to be equal to 1, we have:

x = 2πn, where n is an integer.

So, the general solution to the equation is:

x = 2πn, where n is an integer.