化简:(1+sin4x-cos4x)/(1+sin4x+cos4x) - (1+sin4x+cos4x)/(1+sin4x-cos4x)
来源:学生作业帮助网 编辑:作业帮 时间:2024/09/08 02:16:47
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化简:(1+sin4x-cos4x)/(1+sin4x+cos4x) - (1+sin4x+cos4x)/(1+sin4x-cos4x)
化简:(1+sin4x-cos4x)/(1+sin4x+cos4x) - (1+sin4x+cos4x)/(1+sin4x-cos4x)
化简:(1+sin4x-cos4x)/(1+sin4x+cos4x) - (1+sin4x+cos4x)/(1+sin4x-cos4x)
(1+Sin4x+Cos4x)/(1+Sin4x-Cos4x)
=[1+Sin4x+2(Cos2x)^2-1]/{1+Sin4x-[1-2(Sin2x)^2]}
=[Sin4x+2(Cos2x)^2]/[Sin4x+2(Sin2x)^2]
=[2Sin2xCos2x+2(Cos2x)^2]/[2Sin2xCos2x+2(Sin2x)^2]
=Cos2x/Sin2x
=Cot2x
所以
原式=1/Cot2x - Cot2x