Question

（1／sin10度）－根号3／cos10度

（1／sin10度）－根号3／cos10度

Answer 1

解答：
（1／sin10度）－根号3／cos10度
=1/sin10°-√3/cos10°
=(cos10°-√3sin10°)/(sin10°cos10°)
=2[(1/2)cos10°-(√3/2)sin10°]/(sin10°cos10°)
=4[(1/2)cos10°-(√3/2)sin10°]/(2sin10°cos10°)
=4(cos60°cos10°-sin60°sin10°)/sin20°
=4cos(60+10)°/sin20°
=4cos70°/sin20°
=4

Answer 2

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 3

4