(a+b)^n第k项=Cn(k-1)*a^(n-k+1)*b^(k-1)
所以(x-1/x)^n第3项=Cn2*x^(n-2)*(-1/x)^(2)
所以系数=Cn2=10
n(n-1)/2=10
n^2-n-20=0
显然n>0
所以n=5
sin(x-π/4)=sinxcosπ/4-cosxsinπ/4=√2/2*(sinx-cosx)
cos2x=cos²x-sin²x=(cosx-sinx)(cosx+sinx)
所以cos2x/sin(x-π)=-(cosx+sinx)/(√2/2)=-√2(cosx+sinx)=-√2/2
所以sinx+cosx=1/2