Does the Identity Sin² x + Cos² x = 1 Apply to All Multiples of x?

[basty]

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?

 

[micromass]

Yes.

 

[Mark44]

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.

 

[basty]

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

 

[Mark44]

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

$\sin^2(A) = \frac{1 - \cos(2A)}{2}$
If A = 2x, what is 2A?