Question

1/sin10°-(根号3)/cos10°

过程!

Answer 1

1/sin10°-(根号3)/cos10°
=(cos10°-(根号3)sin10°)/(sin10°×cos10°)
=2(1/2 cos10°- (根号3)/2 sin10°))/(sin10°×cos10°
=2(sin30°cos10°-cos30°sin10°)/(sin10°×cos10°)
=2sin20°/(sin10°×cos10°)
=4sin20°/(2sin10°×cos10°)
=4sin20°/sin20°
=4

Answer 2

通分:
[cos10°-(根号3)sin10°]/sin10°*cos10°
利用公式化间分子分母:
[2(1/2cos10°-(根号3)/2*sin10°)]/(1/2*sin20°)
分子为:2[cos(60°+10°)]
所以=2cos70°/(1/2*sin20°)=2cos70°/(1/2)*cos70°=4