求证:sin^2/(sin-cos) - (sin+cos)/(tan^2 -1) =sin+cos
题目
求证:sin^2/(sin-cos) - (sin+cos)/(tan^2 -1) =sin+cos
答案
sin^2/(sin-cos) - (sin+cos)/(tan^2 -1)
=sin^2/(sin-cos) -(sin+cos)/[(sin^2/cos^2)-1]
=sin^2/(sin-cos) -(sin+cos)cos^2/(sin^2-cos^2)
=sin^2/(sin-cos) -cos^2/(sin-cos)
(sin^2-cos^2)/(sin-cos)
=sin-cos
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