Question

1/sin10°-√3/sin80°

Answer 1

1/sin10-√3/sin80

=(sin80-√3*sin10)/(sin80*sin10)

=(cos10-√3*sin10)/(cos10*sin10)

=4(cos10/2-√3*sin10/2)/(2sin10*cos10)

=4*(cos60*cos10-sin60*sin10)/sin20

=4*cos(60+10)/sin20

=4*cos70/sin20

=4