Question

已知cos(π／4+x）=3／5，17π／12＜x＜7π／4，求（sin2x+2sin^2X)／(1-tanx)的值

急用啊，谁可以帮帮忙的

Answer 1

17π／12＜x＜7π／4
x在III、IV象限
cos(π／4+x）=3／5，π/4+x在第四象限
=2sinxcosx(cosx+sinx)/[cosx-sinx)
=(sin2x/cos2x)(sinx+cosx)^2
sinx+cosx=√2sin(x+π/4)=-4√2/5........1)
sin(π/4+x)=-4/5
2sin(x+π/4)cos(x+π/4)=sin(2x+π/2)=-cos2x
=-12/25
cos2x=12/25............................2)
sin2x=cos^2(x+π/4)-sin^2(x+π/4)
=cos(2x+π/2)
=9/25-16/25=-7/25......................3)
sin2x/cos2x=-7/12
原式=(-7/12)*25/32=-175/384