Question

find the exact value given that cosA=(1/3) in quad I, sin B=(-1/2) in quad 4, and sin C=(1/4) in quad 2

tan(B+C) ?

At the end of my equation I had (sqrt45/15) over (1-sqrt15/15) , how do I rationalize or did I make an error in calculation

Answer 1

you should have had tanB = -1/√3 and tanC = -1/√45

for tan(B+C) I got (-√15 - √3)/(√45 - 1)

(which is the right answer, because I used my calculator to find the actual angles.)

we could change the answer to
(-√15 - √3)/(3√5 - 1) and then multiply top and bottom by (3√5 + 1)/(3√5 + 1) if you have to rationalize it.