Question

Cot (15 degrees)

Part I: Find two common angles that differ by 15 degrees. Rewrite this problem as the cotangent of a difference of those two angles.
Part II: Evaluate the expression (Please show steps)

Answer 1

Part I: cot(15 degrees) = cot(45 - 30)

Part II: Evaluation is below

Explanation:

Everything is done in degrees

Two angles that differ by 15 degrees that is easy to evaluate is 30 degrees and 45 degrees. The cot(15 degrees) = cot(45 - 30) = 1/tan(45-30) = (1+tan45tan30)/(tan30 - tan45) = (1+ sqrt(3))/(sqrt(3) - 1)

We rationalize this by multiplying 1+ sqrt(3) in the top and bottom, getting:

(4 + 2sqrt(3))/2 = 2 + sqrt(3)

I hope this helps! :)