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Prove that Sin^2x + Cos^2x + 1 = 2Cos^2x + 2Sin^2x

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Sin2x + Cos2x + 1                  Given

1 + 1                                    Pythagorean identity (sin2x + cos2x = 1)

2                                         Addition

2*1                                     Identity property of multiplication

2(sin2x + cos2x)                    Pythagorean identity (1 = sin2x + cos2x)

2sin2x + 2cos2x                     Distributive property