You Do Need power plug adapter while traveling from Cook Islands to Bangladesh.

Here is Why You Need An Adapter

The outlet and plug type used in Bangladesh are A, C, D, G and K and in Cook Islands is I. This is how they look like.

Cook Islands

In Cook Islands, outlets of type I are in use.

Type I

Bangladesh

In Bangladesh, outlets of type A, C, D, G and K are in use.

Type A

Type C

Type D

Type G

Type K