Question

化简 根号下1-sin20°/cos10°-根号下1-sin2100°，1-sin2100°的2是在sin上面的

Answer 1

√(1-sin20°)/[cos10°-√(1-sin²100°)]

180°>100°>90°
cos100°<0
sin100°>0
√(1-sin²100°)=-cos100°

cos10°-√(1-sin²100°)=cos10°+cos100°=cos10° + cos(90°+10°)=cos10°-sin10°

1-sin20°=1-2sin10°cos10°=sin²10°+cos²10°-2sin10°cos10°=(cos10°-sin10°)²

原式=√(cos10°-sin10°)²/(cos10°-sin10°)=(cos10°-sin10°)/(cos10°-sin10°)=1

Answer 2

√(1-sin20°) / cos10° - √{1-(sin100°)^2}
= √(sin10°-cos10°)^2 / cos10° - √{1-(sin180°)^2
= (cos10°-sin10°) / cos10° - √{1-(cos10°)^2
= 1-tan10° - sin10°

追问

√{1-(sin100°)^2}怎么变成√{1-(sin180°)^2的？