令 y=3(sinx)^2-(cosx)^2-4cosx+a^2
=3[1-(cosx)^2]-(cosx)^2-4cosx+a^2=3-4(cosx)^2-4cosx+a^2
=a^2+4-(2cosx+1)^2
-1≤cosx≤1 => -1≤2cosx+1≤3 => 0≤(2cosx+1)^2≤9
题中 4≤y≤20 4≤a^2+4-(2cosx+1)^2≤20
=> (2cosx+1)^2≤ a^2≤16+(2cosx+1)^2
=> 0≤a^2≤25
=> -5≤a≤5