Final answer:
To find sin(u/2), cos(u/2), and tan(u/2) using the half-angle formulas, first find the values of sin(u) and cos(u) by using the given information. Then apply the half-angle formulas for sine, cosine, and tangent to find sin(u/2), cos(u/2), and tan(u/2).
Step-by-step explanation:
To find sin(u/2), cos(u/2), and tan(u/2) using the half-angle formulas, we first need to find the values of sin(u) and cos(u). Since cot(u) = 2, we can use the identity cot(u) = 1/tan(u) to find tan(u), which is 1/2. From there, we can find sin(u) and cos(u) using the Pythagorean identity sin^2(u) + cos^2(u) = 1.
sin(u) = sin(arctan(1/2)) = 1/√(1+(1/2)^2)
cos(u) = cos(arctan(1/2)) = 2/√(1+(1/2)^2)
Now we can use the half-angle formulas:
sin(u/2) = ±√((1 - cos(u))/2)
cos(u/2) = ±√((1 + cos(u))/2)
tan(u/2) = sin(u)/(1 + cos(u))