解个三角函数(1-2sin Xcos X)/(cos^2 X-sin^2 X) == (1-tan X)/(1+tan
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解个三角函数
(1-2sin Xcos X)/(cos^2 X-sin^2 X) == (1-tan X)/(1+tan X)
(cos B-1)^2+sin^2 B == 2-2cos B
证明左右相等
(1-2sin Xcos X)/(cos^2 X-sin^2 X) == (1-tan X)/(1+tan X)
(cos B-1)^2+sin^2 B == 2-2cos B
证明左右相等
(1-2sin Xcos X)/(cos^2 X-sin^2 X)
=(sin^2 X-2sin Xcos X+cos^2 X)/(cos^2 X-sin^2 X)
=(sin X-cos X)^2/(cos X-sin X)(cos X-sin X)
=(cos X-sin X)^2/(cos X-sin X)(cos X+sin X)
=(cos X-sin X)/(cos X+sin X)
=(cos X-cos X*tan X)/(cos X+cos X*tan X)
=cos X(1-tan X)/[cos X(1+tan X)]
=(1-tan X)/(1+tan X)
(cos B-1)^2+sin^2 B
=cos^2 B-2cosB+1+sin^2 B
=cos^2 B+sin^2 B-2cosB+1
=1-2cosB+1
=2-2cosB
=(sin^2 X-2sin Xcos X+cos^2 X)/(cos^2 X-sin^2 X)
=(sin X-cos X)^2/(cos X-sin X)(cos X-sin X)
=(cos X-sin X)^2/(cos X-sin X)(cos X+sin X)
=(cos X-sin X)/(cos X+sin X)
=(cos X-cos X*tan X)/(cos X+cos X*tan X)
=cos X(1-tan X)/[cos X(1+tan X)]
=(1-tan X)/(1+tan X)
(cos B-1)^2+sin^2 B
=cos^2 B-2cosB+1+sin^2 B
=cos^2 B+sin^2 B-2cosB+1
=1-2cosB+1
=2-2cosB
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