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