**Find the exact values of sin(u/2), cos(u/2), and tan(u/2) using the half-angle formulas for cot(u) = 3 in quadrant 2**

**Answer:**

cot(u)=3,

tan(u)=1/3,

by applying formula

tan(u)= 2tan(u/2)/1-tan^2(u/2)=1/3

6tan(u/2)=1-tan^2(u/2)

let tan(u/2)=x

then,

6x=1-x^2

x^2+6x-1=0

Now by taking positive sign, tan(u/2) comes to be positive which is not possible as u/2 is in 2 quadrant. hence, only negative sign is considered.

taking negative sign,

x= (-6-√40)/2 = (-6-6.32)/2 = --12.32/2 = -6.16

tan(u/2) = -6.16

sec^2(u/2) = 1+tan^2(u/2)

sec^2(u/2) = 38.94

sec(u/2) = -6.24 (as u/2 is in 2 quadrant)

cos(u/2) = -0.1602

sin(u/2) = cos(u/2)*tan(u/2) = (-0.1602)*(-6.16)

sin(u/2) = 0.9868