Question

Cos^2 2x - sin^2 2x= -1

Answer 1

Решение во вложенном файле.

Answer 2

Let's solve the given trigonometric equation:

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

Using the trigonometric identity cos^2θ - sin^2θ = cos(2θ), we can rewrite the equation as:

cos(4x) = -1

To solve for x, we need to find the values of 4x for which cos(4x) equals -1. In the unit circle, the cosine function equals -1 at π radians (180 degrees) plus any multiple of 2π radians (360 degrees). Thus, we can write:

4x = π + 2nπ

where n is an integer.

To solve for x, we divide both sides by 4:

x = (π + 2nπ)/4

Simplifying the expression:

x = (π/4) + (nπ/2)

So, the general solution for the equation cos^2(2x) - sin^2(2x) = -1 is:

x = (π/4) + (nπ/2), where n is an integer.