解3(sinx)^2-sinxcosx-2(cosx)^2=1
问题描述：
解3(sinx)^2-sinxcosx-2(cosx)^2=1
答
3(sinx)^2-sinxcosx-2(cosx)^2=3sinx)^2+(cosx)^2
2(sinx)^2-sinxcosx-(cosx)^2==0
(2sinx+cosx)(sinx-cosx)=0
2sinx+cosx=0
sinx=-cosx/2
tanx=sinx/cosx=-1/2
x=kπ-arctan(1/2)
sinx-cosx=0
tanx=1
x=kπ+π/4
所以x=kπ-arctan(1/2),x=kπ+π/4
答
3(sinx)^2-sinxcosx-2(cosx)^2=13sin^2x-sinxcosx-2cos^2x=sin^2x+cos^2x2sin^2x-sinxcosx-3cos^2x=0(2sinx-3cosx)(sinx+cosx)=02sinx=3cosx或sinx=-cosx.=>tanx=3/2或tanx=-1.=>x=kπ+arctan(3/2)或x=-π/4+kπ.（k...