Sum of cos²x + cos²2x + ... + cos²nx and sin²x + sin²2x + ... + sin²nx

[D H]

Am I right?

Yes!

 

[Dick]

Does helping the exact same person on the exact same question with the exact same frustration level but in another forum count?

It counts double.

 

[Physicsissuef]

But can you tell me please how did they simplify it?

 

[Dick]

I think you should try it first. I don't see any '2' factors in the final result. So you might start with a double angle formula.

 

[Physicsissuef]

$$\frac{cos^2x-sin^2x+cos^2nx-sin^2nx-cos^2(n+1)x+sin^2(n+1)x-sin^2x-cos^2x}{4sin^2x}$$

$$\frac{-2sin^2x+cos^2nx-sin^2nx-cos^2(n+1)x+sin^2(n+1)x}{4sin^2x}$$

Like this?