求证:tan^2(α)-1/ tan^2(α)=-2sin4α/sin^3(2α)
问题描述：
求证:tan^2(α)-1/ tan^2(α)=-2sin4α/sin^3(2α)
答
左边=tan^2(α)-1/ tan^2(α) = sin^2(α)/cos^2(α) - cos^2(α)/sin^2(α) = (sin^4(α)-cos^4(α)) / (cos^2(α) * sin^2(α)) = (sin^2(α) + cos2^(α))*(sin^2(α) - cos^2(α)) / (cos^2(α) * sin^2(α)) = ...