[三角函數基本公式]

三角函數公式sin^2x+cos^2x=1有沒等於sin^2(4x)+cos^2(4x)=1 sin^2x+cos^2x=sin^2(4x)+cos^2(4x)=1這是沒問題的因為兩邊都等於1 有誤請提醒
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設 sin^2(x) + cos^2(x) =1 for all real x.

x 是 real 則4x 也是 real,
故 sin^2(4x)+cos^2(4x) = 1 for all real x.


反之, 設 sin^2(4x)+cos^2(4x) = 1 for all real x.

x 是 real 則 x/4 也是 real,
故 sin^2(x)+cos^2(x) = sin^2(4*x/4)+cos^2(4*x/4) = 1 for all real x.

2011-04-30 20:07:16 補充：
因此,
sin^2(x)+cos^2(x) = 1 for all real x
if and only if
sin^2(4x) + cos^2(4x) = 1 for all real x.