问题描述: 已知cos(π/4+x)=4/5,x∈(-π/2,-π/4).求(sin2x-2sin²x)/(1+tanx) 1个回答 分类:综合 2014-09-27 问题解答: 我来补答 cos(π/4+X)=4/5,X∈(-π/2,-π/4),则π/4+X∈(-π/4,0),2X∈(-π,-π/2)sin(π/4+X)=-3/5,sin(π/2+2X)=2 sin(π/4+X)cos(π/4+X)=-24/25cos2X =sin(π/2+2X)=sin(π/2-2X)=-24/25,sin2X=-7/25(sin2X-2sin²X)/(1+tanX)=(2sinXcosX-2sin²X)/(1+sinX/cosX)=2sinXcosX(cosX-sinX)/(cosX+sinX)=sin2X(1-sin2X)/cos2X=(-7/25)×(1+7/25)/(-24/25)=28/75 展开全文阅读