express the square root of 3 divided by 1-cos30 degrees in surd form and simplify without using a calculator or mathematical tables

Answer 1

To express the square root of 3 divided by 1 - cos(30 degrees) in surd form and simplify it, we need to make use of the trigonometric identity: 1 - cos(x) = 2sin^2(x/2).

In this case, x = 30 degrees, so we have:

1 - cos(30 degrees) = 2sin^2(30 degrees / 2)

Now, we can substitute this into the expression to get:

√3 / (1 - cos(30 degrees)) = √3 / (2sin^2(30 degrees / 2))

Since sin(30 degrees) = 1/2, we can simplify further:

√3 / (1 - cos(30 degrees)) = √3 / (2(1/2))^2

= √3 / (2(1/4))

= √3 / (1/2)

= √3 * (2/1)

= 2√3

Therefore, the square root of 3 divided by 1 - cos(30 degrees) simplified in surd form is 2√3.