题目内容：

已知3sin x/2-cosx/2等于0 （1）求tanx的值 （2）求cos2x/根号2cos（派/4+x）sinx的值

优质解答

3sinx/2-cosx/2=0
得到tanx/2=1/3
tanx=2tanx/2/(1-tan^2x/2)=(2/3)/(1-1/9)=6/(9-1)=3/4
cos2x/根号2cos(Pai/4+x)sinx
=cos2x/根号2(cosx*根号2/2-sinx*根号2/2)sinx
=cos2x/(cosxsinx-sin^2 x)
=(cos^2x-sin^2x)/(cosxsinx-sin^2x)
=(1-tan^2x)/(tanx-tan^2x)
=(1-9/16)/(3/4-9/16)
=(16-9)/(12-9)
=7/3