Rozw. dla cos3p
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sin3p=sin(p+2p)=sinpcos2p+cospsin2p=
stosujemy wzory
cos2x=cos^2x-sin^2x=1-2sin^2x=2cos^2x-1
cos^2x=1-sin^2x
…
=sin(1-2sin^2p)+cosp*2sinpcosp=
=sinp-2sin^3p+2cos^2sinp=
=sinp-2sin^3p+2(1-sin^2p)sinp=
=sinp-2sin^3p+2sinp-2sin^3p=
=3sinp-4sin^3p