Question

求函数f(¤)=[(sin¤)-1]/[(cos¤)-2]的最大值和最小值 注：¤表示角

Answer 1

运用万能公式设tan(A/2)=t

sinA=2t/(1+t^2)

cosA=(1-t^2)/(1+t^2)

代入化简得y=(t-1)^2/(3t^2+1)

y'=2(t-1)(3t-1)/(3t^2+1)^2

t=1/3时有最大值1/3

t=1时有最小值0