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

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

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`2(cos^4x+sin^4x)`
`=2((cos^2x)^2+(sin^2x)^2)`
`=2((cos^2x+sin^2x)−2sin^2xcos^2x)`
`=2−4sin^2xcos^2x`
...
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