Question

Express 1+cos 30°/1-sin 30°

Answer 1

You MUST know the trig ratios of the 30-60-90 triangles by heart
sin 30° = 1/2, cos30° = √3/2

Assuming you meant
(1+cos 30°)/(1-sin 30°)
= (1 + √3/2) / (1 - 1/2)
= (1 + √3/2)(2)
= 2 + √3

Answer 2

or, using your half-angle formulas, that is cot(15°)