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prove that : sin^4x+cos^4x=1-1/2sin^2 ...

prove that : `sin^4x+cos^4x=1-1/2sin^2 2x`

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`LHS= (cos^(2) x+ sin^(2) x)^(2) -2 cos^(2) x sin^(2) x`
` =1-2 cos^(2) x sin^(2) x =1-(1)/(2) (sin^(2) 2x) =(1)/(2)(2 -sin^(2) 2x) =RHS`
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