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prove cos 6 x = 1/32(cos 6x + 6 Cos 4x + 15 Cos 2x + 10) prove cos6x = 1/32(cos 6x + 6 Cos 4x + 15 Cos 2x + 10)
I have solved it with a simple and smart approach. cos^6x=((e^ix+e^-ix)/2)^6 =1/2^6(e^6ix+6e^5ixe^-ix+15e^4ixe^-2ix +20e^3ixe^-3ix+15e^2ixe^-4ix +6e^ixe^-5ix+e^-6ix) =1/32(((e^6ix+e^-6ix)/2) +6((e^4ix+e^-4ix)/2) +15((e^2ix+e^-2ix)/2) +10) cos^6x=1/32(15cos2x +6cos4x +cos6x +10)
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