Question

y=1-2sin平方x+2cosx 求值域

Answer 1

y=1-2sin^2x+2cosx

=1-2sin^2x+2cosx=2(cosx)^2-1-2cosx

令cosx=t ,-1≤t≤1

y=2t^2-2t-1

=2(t-1/2)^2-3/2

当t=1/2时,y有最小值 -3/2

当t=-1时,y有最大值 3

-3/2≤y≤3