若α∈(-3π/4,-π/2),且(2sin^2α+sin2α)/(1+tanα)=k,y=sinα-cosα.则用k表
题目
若α∈(-3π/4,-π/2),且(2sin^2α+sin2α)/(1+tanα)=k,y=sinα-cosα.则用k表
若α∈(-3π/4,-π/2),且(2sin^2α+sin2α)/(1+tanα)=k,y=sinα-cosα.则用k表示y
答案
k=(2sin^2α+sin2α)/(1+tanα)
=2sinα( sinα+cosα)/【(sinα+cosα)/ cosα】
= 2sinαcosα
= sin2α
由α∈(-3π/4,-π/2)可知y
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