Question

1/sin10°-根号3/cos10°=

Answer 1

1/sin10°-根号3/cos10°
=(cos10-根3*sin10)/(sin10*cos10)
=4*(sin150*cos10+sin10*cos150)/sin20
=4*sin160/sin20
=4

Answer 2

1/sin10-√3/cos10
=2*(sin30/sin10-cos30/cos10)
=2(sin30cos10-sin10cos30)/(sin10cos10)
=4(sin(30-10))/sin20
=4

Answer 3

1/sin10°-√3/cos10°
=(cos10°-√3sin10°)/(sin10°*cos10°)

cos10°-√3sin10°
=2(1/2*cos10°-1/2*√3sin10°)
=2*(cos60°*cos10°-sin60°*sin10°)
=2*ocs(60°+10°)=2cos70°=2sin20°

sin10°*cos10°=1/2*sin20°

原式=2sin20°/(1/2*sin20°)
=4