find the exact value of the expression using the provided information. Find Tan (S+T) given that cos s=1/3 with s in quad I and sin T= -1/2 with T in quad IV

Answer 1

s is in Q1 (sin>0, cos>0)
so
cos(s)=1/3,
sin(s)=+√(1-(1/3)²)
=√(8/9)
tan(s)=√(8/9) / (1/3)
=√8

t is in Q4 (sin<0, cos>0)
sin(t)=-1/2
cos(t)=+√(1-(1/2)²)
=√(3/4)
tan(t)=(-1/2)/√(3/4)
=-1/√3
[rationalize by multiplying numerator and denominator by √3]
=-(√3)/3

Use the identity
tan(s+t)=(tan(s)+tan(t))/(1-tan(s)tan(t)) to calculate tan(s+t)
I get about 0.85.