Question

如何求cos20°/cos35°√(1-sin20°)的值

Answer 1

√(1-sin20°)=√((sin20°)^2+(cos20°)^2-2sin10°*cos10°)=cos10°-sin10°
=cos10°-cos80°=-2sin45°sin(-35° )
cos20°/cos35°=sin70°/cos35°=2sin35°
原式=2sin35°/(cos10°-sin10°) =sin45°=√2/2

Answer 2

cos20°/cos35°√(1-sin20°)
= (cos10° ^2 - sin10°^2 ) / ( cos10°- sin10° ) / cos(45°-10°)
= ( cos10°+sin10° ) / [√2 /2 ( cos10°+ sin10° ) ]
= √2