Question

Cos^2 2x = 1+ sin^2 2x​

Answer 1

$cos^22x=1+sin^22x\\cos^22x-sin^2x=1\\cos(2*2x)=1\\cos4x=1\\4x=2\pi n, n\in Z\\x=\frac{\pi n}{2}, n\in Z$

Answer 2

To solve the equation cos²(2x) = 1 + sin²(2x), we can use the trigonometric identity:

sin²(x) + cos²(x) = 1

Let's substitute 2x for x in the equation:

sin²(2x) + cos²(2x) = 1

Now we can rewrite the equation as:

1 + sin²(2x) = 1 + sin²(2x)

Since the equation is an identity, it holds true for all values of x. Therefore, there are infinitely many solutions to this equation.