Question

show that 1/sin10-root3/cos10=4

Answer 1

1/ sin10° - √3 /cos10°

=> (cos10° -√3.sin10°)/sin10°.cos10°

use
sin2A =2sinA.cosA
and sin(A-B) =sinA.cosB -cosa.sinB

now,
=> 4(1/2cos10° -√3/2sin10°)/2sin10°.cos10°

=> 4{sin30°.cos10° -cos30.sin10°}/sin20°

=>4sin(30°-10°)/sin20°

=>4sin20°/sin20°

=>4 = RHS