1.(2010•
山东青岛模拟)cos 43°cos 77°+sin 43°•cos 167°的值为________.解析 原式=cos 43°cos 77°+sin 43°cos(90°+77°) =cos 43°cos 77°-sin 43°sin 77° =cos(43°+77°)=cos 120°=-12. 答案 -12 2.(2010•南京模拟)已知α、β均为锐角,且cos(α+β)=sin(α-β),则tan α=________. 解析 ∵cos(α+β)=sin(α-β), ∴cos αcos β-sin αsin β=sin αcos β-cos αsin β,即cos β(sin α-cos α)+sin β(sin α-cos α)=0, ∴(sin α-cos α)(cos β+sin β)=0, ∵α、β均为锐角, ∴cos β+sin β>0,∴sin α-cos α=0, ∴tan α=1. 答案 1 3.(2009•湖北四校联考)在△abc中,3sin a+4co