灵鹊做题网求证明,三角函数的,
来源：学生作业帮 编辑：灵鹊做题网作业帮 分类：数学作业 时间：2024/04/29 05:13:31
求证明,三角函数的,
(1)
(1-2sinxcosx)/(cos^2 x-sin^2 x)=(cosx-sinx)^2/[(cosx+sinx)(cosx-sinx)]
=(cosx-sinx)/(cosx+sinx)【分子分母再同除以cosx】
=(1-tanx)/(1+tanx)
(2)
tan^2 α-sin^2 α=(sin^2 α/cos^2 α)-sin^2 α
=sin^2 α*[1/cos^2 α-1]【将分子的1用sin^2 α+cos^2 α代替】
=sin^2 α*[(sin^2 α+cos^2 α)/cos^2 α-1]
=sin^2 α*[(sin^2 α/cos^2 α)+1-1]
=sin^2 α*tan^2 α
(1-2sinxcosx)/(cos^2 x-sin^2 x)=(cosx-sinx)^2/[(cosx+sinx)(cosx-sinx)]
=(cosx-sinx)/(cosx+sinx)【分子分母再同除以cosx】
=(1-tanx)/(1+tanx)
(2)
tan^2 α-sin^2 α=(sin^2 α/cos^2 α)-sin^2 α
=sin^2 α*[1/cos^2 α-1]【将分子的1用sin^2 α+cos^2 α代替】
=sin^2 α*[(sin^2 α+cos^2 α)/cos^2 α-1]
=sin^2 α*[(sin^2 α/cos^2 α)+1-1]
=sin^2 α*tan^2 α