Prove the following
(cos x - sin x)(cos 2x - sin 2x) = cos x - sin 3x
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Step-by-step explanation:
LHS
(cosx-sinx)(cos2x-sin2x)
=(cosx-sinx)(1-2sin²x-2sinxcosx)
=cosx-2sin²xcosx-2sinxcos²x-sinx +2sin³x+2sin²xcosx
=cosx-2sinx(1-sin²x)-sinx+2sin³x
=cosx--2sinx+2sin³x-sinx+2sin³x
=cosx-3sinx+4sin³x
=cosx-sin3x
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