已知函数f(x)=(1+cotx)sin^2x+msin(x+π/4)sin(x-π/4).当tanα=2时,f(α）=3/5,求m的值.
问题描述：
已知函数f(x)=(1+cotx)sin^2x+msin(x+π/4)sin(x-π/4).当tanα=2时,f(α）=3/5,求m的值.
答
cot(α)=1/2,
(cscα)^2=1+1/4=5/4,
(sinα)^2=4/5,
f(α)=(1+1/2)*(4/5)+m[(sinα)^2-(cosα)^2]/2
=6/5-(mcos2α)/2
=6/5-m*[1-2(sinα)^2]/2
=6/5-m(1-8/5)/2
=6/5+3m/10
6/5+3m/10=3/5,
m=-2.