已知tanx=2求2sinx-3cosx/4sinx-9cosx;sin平方x-sinx.cosx=1的值

2sinx-3cosx/4sinx-9cosx=2tanx-3/4tanx-9=-1sin²x-sinxcosx=1-cos2x/2-1/2sin2x=-(1/2cos2x+1/2sin2x)+1/2=-sin(2x+π/4)+1/2=1∴sin(2x+π/4)=-1/2∴2x+π/4=2kπ-π/6∴x=kπ-5π/24