Question 746701
Given: angles A and B are in Quadrant I, where
tanA = 1/7 sinB= 5/SQRT74 
Find the exact value of tan(A+B).
{{{sin(B)=5/sqrt(74)}}}
{{{cos(B)=sqrt(1-sin^2(B))=sqrt(1-25/74)=sqrt(49/74)=7/sqrt(74)}}}
tanB=sinB/cosB=5/7
tan(A+B)=(tanA+tanB)/(1-tanAtanB)
=(1/7+5/7)/(1-1/7*5/7)=6/7/(1-5/49)
=(6/7)/(44/49)
=294/308
Check: (with calculator)
tanA=1/7
A≈8.1301º
sinB=5/√74
B≈35.5377º
A+B≈43.6678
tan(A+B)≈tan(43.6678º)≈0.9545..
Exact ans.=294/308≈0.9545..