Why does 3x = x?

[KindofSlow]

Book says:
sin^2(3x) + cos^2(3x) = sin^2(x) + cos^2(x), which of course equals 1 as it is a pythagorean identity.
I cannot figure out why we are allowed to just drop the coefficient 3 and say that, in this situation, 3x = x.
Any clarification will be appreciated.
Thank you

 

[BigGlenntheHeavy]

\(\displaystyle Where \ do \ you \ get \ 3x \ = \ x?\)

 

[KindofSlow]

From: sin^2(3x) + cos^2(3x) = sin^2(x) + cos^2(x).
Everything is the same except the 3x becomes an x.

 

[lookagain]

From: sin^2(3x) + cos^2(3x) = sin^2(x) + cos^2(x).
Everything is the same except the 3x becomes an x.

No, just because the function values are equal for two x-values does not mean the x-values are equal
to each other.

Example:

\(\displaystyle (-1)^2 = (1)^2,\) but we know that \(\displaystyle -1 \ne 1\).

 

[KindofSlow]

Aha, very helpful, thank you