Solve: sin(x)+sin(2x)+sin(3x)= 1 +cos(x)+cos(2x)

[Aladdin]

Math Homework:
(Linearization formulas)
sin(x)+sin(2x)+sin(3x)= 1 +cos(x)+cos(2x)

 

[fasteddie65]

Re: Solve:

sin x + sin 2x + sin 3x = 1 + cos x + cos 2x

sin x + sin 2x + sin 3x = sin x + 2 sin x cos x + 3 sin x cos^2 x - sin^3 x

1 + cos x + cos 2x = 1 + cos x + 1 - 2 cos^2 x

By the way, this is not an identity.

Some solutions are ?/6, ?/2, 2?/3, 5?/6, 4?/3, 3?/2, etc.

 

[Aladdin]

Re: Solve:

sin x + sin 2x + sin 3x = 1 + cos x + cos 2x

sin x + sin 2x + sin 3x = sin x + 2 sin x cos x + 3 sin x cos^2 x - sin^3 x

1 + cos x + cos 2x = 1 + cos x + 1 - 2 cos^2 x

By the way, this is not an identity.

Some solutions are ?/6, ?/2, 2?/3, 5?/6, 4?/3, 3?/2, etc.

Thank you for your help , I appreciate thanks