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## Homework Statement

Prove that:

[itex] \cos^6{(x)} + \sin^6{(x)} = \frac{5}{8} + \frac{3}{8} \cos{(4x)} [/itex]

## Homework Equations

I am not sure. I used factoring a sum of cubes.

## The Attempt at a Solution

I tried [itex] \cos^6{(x)} + \sin^6{(x)} = \cos^4{(x)} - \cos^2{(x)} \sin^2{(x)} + \sin^4{(x)} [/itex]. But I can't get anywhere beyond this; I must be missing something obvious.