Question

求函数y=(sin x+1)(cos x+1)的最值

Answer 1

y=sinxcosx+sinx+cosx+1

(sinx+cosx)^2=1+2sinxcosx

sinxcosx=((sinx+cosx)^2-1)_/2

设sinx+cosx=t

sinxcosx=(t^2-1)/2

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

=1/2t^2+t+1/2

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

1/2(t+1)^2

t=2^1/2sin(x+pai/4)

-2^1/2