Question

Show that 1/sin10-√3/cos10=4

Answer 1

1/sin10-√3/cos10
= (cos10 - √3sin10)/cos10sin10
multiplying 1/2 in denominator and numerator
= {(cos10/2) - (√3sin10/2)}/(cos10sin10/2)
= (cos60cos10 - sin60sin10)/(cos10sin10/2)
= cos(60 + 10)/(cos10sin10/2)
= cos70/(cos10sin10/2)
= 2cos70/cos10sin10
multiplying 2 on numerator and denominator
= 4cos70/2sin10cos10
=4cos70/sin20
=4cos70/cos70
= 4 proved