Question

求{sin}^{2}α-{cos}^{2}α+3sinαcosα的最值

Answer 1

{sin}^{2}α-{cos}^{2}α+3sinαcosα=(3/2)sin2α-cos2α,所以最大值是

根号下((3/2)^2+(-1)^2) = (根号13)/2,最小值是 -(根号13)/2