Does the Pythagorean identity hold for sin(3x) and cos(3x)?

[teng125]

as we know that (sin(x))^2 + (cos(x))^2=1
how about (sin(3x))^2 + (cos(3x))^2 and 5sin(3x)^2 + 6cos(3x)^2??

how can we solve these problems??
thanx

 

[*melinda*]

What are you trying to solve? You could substitute numbers for the x's and compute the value.

I don't believe there's a nifty identity for (sin(3x))^2 + (cos(3x))^2 even though it does look somewhat similar to (sin(x))^2 + (cos(x))^2.

 

[*melinda*]

Actually, aslong as the arguments match it equals one. So (sin(3x))^2 + (cos(3x))^2 does equal one.

 

[Hootenanny]

Indeed, if we apply the identity $\sin^{2}\theta +\cos^{2}\theta = 1$,to the above expression and simply use the substitution $3x = \theta$...

 

[HallsofIvy]

For 5sin(3x)^2 + 6cos(3x)^2, write it as 5sin^3(3x)+ 5cos^2(3x)+ cos^2(3x)= 5(sin^3(3x)+ cos^2(3x))+ cos^2(3x)= 5+ cos^2(3x).