# Trigonometry sin cos Question

I know that ##\sin^2 x + cos^2 x = 1.##

Is this mean that

##\sin^2 2x + \cos^2 2x = 1##

or

##\sin^2 3x + \cos^2 3x = 1##

or

##\sin^2 4x + \cos^2 4x = 1##

and so on?

Yes.

Mark44
Mentor
I know that ##\sin^2 x + cos^2 x = 1.##

Is this mean that

##\sin^2 2x + \cos^2 2x = 1##

or

##\sin^2 3x + \cos^2 3x = 1##

or

##\sin^2 4x + \cos^2 4x = 1##

and so on?
##sin^2(\text{whatever}) + cos^2(\text{whatever}) = 1##
The "whatever" in both places has to be the same, of course.

Does ##\sin^2 2x = \frac{1 - \cos 4x}{2}?##

Mark44
Mentor
Does ##\sin^2 2x = \frac{1 - \cos 4x}{2}?##
##\sin^2(A) = \frac{1 - \cos(2A)}{2}##
If A = 2x, what is 2A?