Question

已知tanx=2,求2sin2x-sinxcosx cos2x

Answer 1

分两部分求

2sin2x=4sinxcosx 注：sin2x=2sinxcosx

=4sinxcosx / {(cosx)^2+(sinx)^2} 注：{(cosx)^2+(sinx)^2=1

=4tanx / {1+(tanx)^2} 注：分子分母同时除以(cosx)^2

sinxcosx cos2x=1/2sin2xcos2x 注：sinxcosx=1/2sin2x

=1/2sin2xcos2x / {(cos2x)^2+(sin2x)^2} 注：{(cos2x)^2+(sin2x)^2=1

=1/2tan2x / {1+(tanx)^2} 注：分子分母同时除以(cos2x)^2

tan=2 tan2x=（2tanx）/{1-(tanx)^2}=-(4/3) 数字代入计算一下就可以了

2sin2x-sinxcosx cos2x=26/15