Use double-angle identities to verify that cos (3x) = cos x(1 − 4sin2x.

here are the steps for the proof

Step-by-step explanation:

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L.H.S

=cos (3x)

=cos (x+2x)

=cosxcos2x - sinxsin2x

=cosxcos2x - 2sin^2xcosx

=cosx [cos2x - 2sin^2x]

=cosx [1-2sin^x-2sin^x]

=cosx [ 1-4sin^2x]

=R.H.S

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