Solve 3cos^2(3x)+3sin^2(3x)=3: Trig Identities

[mathguyz]

Everyone knows the obvious trig identities like sin^2 + cos^2 =1, cosx=1+ sin^2, and tanx =sin/cos. I ran across an old identity the other day: 3cos^2(3x)+3sin^2(3x)=3. Can anyone here figure out why and how? I tried it and couldn't figure it out.

 

[jamesrc]

Look at your first "obvious trig identity"...

 

[Marin]

3cos^2(3x)+3sin^2(3x)=3[cos^2(3x)+sin^2(3x)] , now substitude 3x=z and using sin^2(z) + cos^2(z) =1 you have it!

NB: I´m not sure this is correct, whatever it is meant to be: cosx=1+ sin^2