Q. 244.2( 146 Votes )

Prove that cos 4x

Answer :

To prove cos 4x = 1 – 8sin2 x cos2 x

RHS = 1 – 8sin2 x cos2 x


LHS = cos 4x


= cos 2(2x)


= 1 – 2 sin2 2x [cos 2A = 1 – 2 sin2 A]


= 1 – 2(2 sin x cos x)2[sin2A = 2sin A cosA]


= 1 – 8 sin2 x cos2 x


LHS = RHS


Hence, proved.


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