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Prove that cos 4(x)=1-8 sin ^(2) (x) cos...

Prove that `cos 4(x)=1-8 sin ^(2) (x) cos ^(2) (x)`

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( L.H.S ) =cos 4 x=cos 2(2 x) =1-2 sin ^(2) 2 x=1-2(sin 2 x)^(2)=1-2(2 sin dot(x) cos x)^(2) , =1-8 sin ^(2) x cos ^(2) x= ( R.H.S. ) .
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