Question

化简根号下(1-2sin10°cos10°)/[cos10°-根号下(1-sin^2 80°)]

Answer 1

根号下(1-2sin10°cos10°)/[cos10°-根号下(1-sin^2 80°)]
=根号下(sin10°-cos10°)^2/[cos10°-根号下(cos^2 80°)]
=|sin10°-cos10°|/[cos10°-cos80°] cos10°>sin10° cos80°=sin10°
=(cos10°-sin10°)/(cos10°-sin10°)
=1

Answer 2

=(sin²10°-2sin10°cos10°+cos²10°)/(cos10°-√cos²80°)
=(sin10°-cos10°)²/(cos10°-cos80°)
=(cos10°-sin10°)²/(cos10°-sin10°)
=cos10°-sin10°

Answer 3

原式=√(sin²10+cos²10-2sin10cos10)/[cos10-√cos²80]
=√(sin10-cos10)²/(cos10-cos80)
=|sin10/cos10|/(cos10-sin10)
=(cos10-sin10)/(cos10-sin10)
=1