Use the halfangle identities to find the desired function va

Use the half-angle identities to find the desired function value. Assume that x >/= to 0.

If cos x = -1/4 and csc x < 0, find cot(x/2)

cos x = -1_/4 and csc x < 0

=>x is in third quadrant

<=x<=3_/2

=>_/2<=x_/2<=3_/4

=>x_/2 is in second quadrant

=>sin(x_/2)>0, cos(x_/2)<0

sin(x_/2)=((1_/2)[1-cosx]),cos(x_/2)=-((1_/2)[1+cosx])

=>sin(x_/2)=(1_/2)[1-(-1_/4)],cos(x_/2)=-((1_/2)[1+(-1_/4)])

=>sin(x_/2)=(5_/8),cos(x_/2)=-(3_/8)

cot(x_/2)=cos(x/2)_/sin(x/2)

cot(x_/2)=-(3/8)_/_(5/8)

cot(x_/2)=-(3_/5)