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Prove that cos 6 x=32 cos ^(6) x-48 cos ...

Prove that `cos 6 x=32 cos ^(6) x-48 cos ^(4) x+18 cos ^(2) x-1`

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( L.H.S. )=cos 6 x=2 cos ^(2) 3 x-1 (because cos 2 theta=2 cos ^(2) theta-1) = 2(cos 3 x)^(2)-1=2(4 cos ^(3) x-3 cos x)^(2)-1 = 2(16 cos ^(6) x-24 cos ^(4) x+9 cos ^(2) x)-1 = 32 cos ^(6) x-48 cos ^(4) x+18 cos ^(2) x-1= ( R.H.S. ) .
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