Prove that Cos(3x)=4Cos³x-3Cosx
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Step-by-step explanation:
cos (2x+x) = cos2x cosx - sin2x sinx
. = (2cos²x - 1) cosx - 2sinxcosx.sinx
= 2cos³x - cosx - 2sin²xcosx
= 2cos³x - cosx - 2( 1 - cos²x ) cosx
[sin²x + cos²x = 1] ; sin²x = 1 - cos²x
= 2cos³x - cosx - 2cosx + 2 cos³x
= 4 cos³x - 3cosx