求函数y=cosx+cos(x-π3)(x∈R)的最大值和最小值.

问题描述:

求函数y=cosx+cos(x-

π
3
)(x∈R)的最大值和最小值.

∵y=cosx+cos(x-

π
3

=cosx+cosxcos
π
3
+sinxsin
π
3

=
3
2
cosx+
3
2
sinx
=
3
(cos
π
6
cosx+sin
π
6
sinx)
=
3
cos(x-
π
6
),
∵-1≤cos(x-
π
6
)≤1,
∴ymax=
3
,ymin=-
3