Question

prove that 4cosx.cos(^/3+x)cos (^/3-x)=cos3x​

Answer 1

hello mate ♥♥♥♥♥♥♥♥.How would you prove 4cosxcos (60 +X) cos (60–X) =cos3x?
4cosx.cos(60+x).cos(60-x)=cos3x

LHS. 2cosx.[2cos(60+x).cos(60-x)]

=2cosx[cos(60+x+60-x)+cos(60+x-60+x)]

=2cosx[cos 120+cos 2x]

=2cos x[ -1/2 +cos 2x]

=-cos x+2cos 2x.cos x

=-cos x +cos (2x+x) +cos(2x-x)

=-cos x+cos 3x +cos x

=cos 3x proved.