已知tanx=2,求2sin2x-sinxcosx cos2x
2个回答

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