已知函数f(X)=(1+1/tanx)sin^2x+msin(x+π/4)sin(x-π/4) 当tana=2时,f（a)=3/5,求m的值

已知函数f(X)=(1+1/tanx)sin^2x+msin(x+π/4)sin(x-π/4) 当tana=2时,f（a)=3/5,求m的值
已知函数f(X)=(1+1/tanx)sin^2x+msin(x+π/4)sin(x-π/4) 当tana=2时,f（a)=3/5,求m的值

已知函数f(X)=(1+1/tanx)sin^2x+msin(x+π/4)sin(x-π/4) 当tana=2时,f（a)=3/5,求m的值
将函数f(X)=(1+1/tanx)sin^2x+msin(x+π/4)sin(x-π/4) 化简得：=(1+cosx/sinx)*2sinxcosx+m(sinxcosπ/4+cosxsinπ/4)(sinxcosπ/4-cosxsinπ/4) =2sinxcosx+2(cosx)^2+1/2[(sinx)^2-(cosx)^2]m 由tana=2得 sina=2cosa 所以：f(a)=(sina)^2+2(cosa)^2+1/2*3m(cosa)^2 =1+(cosa)^2+3m/2*(cosa)^2 =3/5 所以得：3m/2*(cosa)^2+2/5[(cosa)^2+(sina)^2]+(cosa)^2=0 3m/2*(cosa)^2+7/5*(cosa)^2+2/5*(sina)^2=0 因为tana=2 将上式同除于(cosa)^2得（(cosa)^2由tana=2知不会为零）：3m/2+7/5+2/5*4=0 所以：m=-2