Q. 14

# Prove the following identities:cos3 2x + 3 cos 2x = 4(cos6 x – sin6 x)

Proof:

Take RHS:

{ a3 – b3 = (a – b) (a2 + b2 + ab)}

{ cos 2x = cos2 x – sin2 x}

{ a2 + b2 + 2ab = (a + b)2}

{ cos2 x + sin2 x = 1}

{ sin 2x= 2 sin x cos x}

{ sin2 x = 1 – cos2 x}

= LHS

Hence Proved

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