Prove that 12 cos(30°) - 2 tan(60°) can be written as √k where k is an integer, state the value of k.
Conversion of trigonometric functions:
cos(30°) = √3 / 2
tan(60°) = √3
Computing equation with trigonometric substitutions:
12 cos(30°) - 2 tan(60°) = 12 (√3 / 2) - 2 (√3) = (12 / 2) x √3 - 2√3 = 6√3 - 2√3 = 4√3
Rearranging into requested form:
4√3 = √42 x √3 = √16 x √3 = √48
Stating k:
√k = √48
k = 48
