化简:根号(1-2sin100°cos280°)/{cos370°-根号[1-cos^2(170°)]}

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/06 03:24:52
化简:根号(1-2sin100°cos280°)/{cos370°-根号[1-cos^2(170°)]}

化简:根号(1-2sin100°cos280°)/{cos370°-根号[1-cos^2(170°)]}
化简:根号(1-2sin100°cos280°)/{cos370°-根号[1-cos^2(170°)]}

化简:根号(1-2sin100°cos280°)/{cos370°-根号[1-cos^2(170°)]}
sinαcosβ = [sin(α+β)+sin(α-β)]/2
所以sin100cos280 = [sin(α+)+sin(α-β)]/2=sin20/2
根号(1-2sin100°cos280°)=根号(1-sin20)=根号(1-2sin10cos10)=cos10-sin10
根号[1-cos^2(170°)]=sin(170°)=cos(80°)
cos370°=cos10°
cos370°-根号[1-cos^2(170°)]=cos10°-cos(80°)=cos10-sin10
所以结果为1