root3/1-cos30

Question

leave your answer in surd form

Answer 1

well, I happen to remember that sin 30 = 1/2
so draw a right triangle with small side 1 and
hypotenuse 2
then the big side is sqrt(4-1) = sqrt3
so
cos 30 = sqrt3 / 2
so
sqrt3 / (1 - sqrt3 / 2) = 2 sqrt3 /(2-sqrt3)
=2 sqrt3 /(2-sqrt3) * (2+sqrt3)/(2+sqrt3)
=(4 sqrt3 + 3) / (4-3)
= 4 sqrt3 + 3

Answer 2

=2 sqrt3/(2-sqrt3)*(2+sqrt3)/(2+sqrt3)
is going to be equal to (4 sqrt3+6)/(4-3)
=4 sqrt3 + 6
thank you though. I didn't know how it was supposed to be done.🙏