(1)把f(x)变形为
f(x)=2t2-6t+3-(sinx+t)^2
当t>1时,f(x)的最小值g(t)=2t2-6t+3-(-1+t)^2=t2-4t+2
当t<1时,f(x)的最小值g(t)=2t2-6t+3-(1+t)^2=t2-8t+2
当-1≤t≤1时,f(x)的最小值g(t)=2t2-6t+3
(2)
-1≤t≤1时,g(t)=2t2-6t+3
2t2-6t+3=kt
k=2t+3/t-6
当-1≤t≤0
-2t-3/t≥2√6
2t+3/t-6≤-2√6-6
k≤-2√6-6
当0≤t≤1
2t+3/t≥2√6
2t+3/t-6≥2√6-6
k≥2√6-6
所以k≤-2√6-6或k≥2√6-6