已知tanx=2,则(1)1/4sin方x-3sinxcosx/cos方x+2sinxcosx

问题描述:

已知tanx=2,则(1)1/4sin方x-3sinxcosx/cos方x+2sinxcosx

(1)=(1/4)sin^2x-3sinx/cosx+2sinxcosx(1)同时除于cos^2x=(1/4)tan^2x-3tanx/cos^2x+2tanx=(1/4)tan^2x-3tanx/[1/(1+tan^2x)]+2tanx=(1/4)tan^2x-3tanx(1+tan^2x)+2tanx=(1/4)*4-3*2(1+4)+4=1-30+4=-25