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England have already recorded a clean sweep victory in the three-match one-day international series but can expect to be worked by the host team's spinners in the Tests.
"We've already seen how well they can play, their spinners will be a huge threat and for us to take them lightly would be a cardinal sin. If we take Bangladesh lightly then we will come unstuck," Cook told reporters.
One man Cook need not worry about is batsman Raqibul Hasan, whose unbeaten century in a three-day warm-up match against England this week forced a Test call-up, only for the 22-year-old to announce his surprise international retirement on Wednesday.
England are the only Test playing side never to lose to Bangladesh in any form of game. Hoping to change that, the hosts have named three left-arm spinners in their squad to try and capitalise on England's traditional weakness against tweakers.
"The way we dealt with spin in the one-dayers was excellent and hopefully we can continue on like that for the next two weeks," Cook, who is standing in for regular captain Andrew Strauss who missed the tour, added.
"We all know spin is important in the sub-continent, playing spin well for long periods of time. Spin is a huge issue and the England side over the last three or four years has a made a huge effort to improve on that," he said.
England are expected to field two off spinners - Graeme Swann and uncapped James Tredwell - in the first Test, but they are struggling with their pace attack.
Ryan Sidebottom has returned home after a thigh injury and one of their first-choice pacers Graham Onions will miss the first Test with a back injury.
Stuart Broad, another frontline seamer, is also suffering from a back spasm and will be assessed ahead of the first Test.
After making just 69 runs in his seven innings on the tour, Bangladesh will be hoping that out-of-form batsmen Kevin Pietersen continues to misfire.
"I hope he keeps failing because it'll be one less batsman to worry about, but he's a great player. At some point in the next four innings he'll have a performance and hopefully it won't hurt us," Bangladesh coach Jamie Siddons said.
"We've got to get through 10, 11 batsmen, KP is just one of them. If he struggles against left-armers, he's got two bloody good ones against him," he said.
The second Test will start in Dhaka on March 20.
