Trigonometric identities

Question

If

Sin²x + sinx = 1

Then what is

Cos¹²x + 3 cos¹⁰x + 3 cos⁸x + cos⁶x = ?

Answer 1

The equation with sin has only one acceptable root: sin x = (1/2)(-1+√5).

You can compute the cos from that and plug in into the equation with cos.

I am not sure this is the answer you were looking for, but I hope it helps.