Find the exact values of sinu2 cosu2 and tanu2 using the hal

Find the exact values of sin(u/2), cos(u/2), and tan(u/2) using the half-angle formulas

cot u = 2, pi<u<3pi/2

Sin(u/2)=

cos(u/2)=

tan(u/2)=

cot u=2

Here adjacent=2 and opposite=1

hypotenuse=sqrt(4+1)=sqrt5

And in third quadrant cos in negative

Therefore cos u=-2/sqrt5

sin u/2=sqrt(1-cos u)/2 = sqrt(1+2/sqrt5)/2=1/10(sqrt(5+2sqrt5)10)

cos u/2= sqrt(1+cos u)/2 = -sqrt(1-2/sqrt5)/2=1/10(sqrt(5-2sqrt5)10)

tan u/2=sin u/2/cos u/2= -sqrt((5+2sqrt5)/(5-2sqrt5))