Thread: Proving of trigonometric ID

Good Day,

I'm stuck on proving the following trigonometric identity:

(sin 2x + sin 4x + sin 6x) / (cos 2x + cos 4x + cos 6x) = tan 4x

I do hope that some one can give me some advice on how to prove this as I've been going at this for the past 2 days and I feel that I'm not getting anywhere near.

Thanks in advance.

Originally Posted by dd86

Good Day,

I'm stuck on proving the following trigonometric identity:

(sin 2x + sin 4x + sin 6x) / (cos 2x + cos 4x + cos 6x) = tan 4x

I do hope that some one can give me some advice on how to prove this as I've been going at this for the past 2 days and I feel that I'm not getting anywhere near.

Use the sum-to-product identities,





We have












Please note, however, that the cancellation step is not valid when The identity actually does not hold for these values of as the original expression is undefined at such values. So the equation is only identically true for

Hi Reckoner,

Thanks so much. Now it's clear where I went wrong.