SOLUTION: Given: angles A and B are in Quadrant I, where tanA = 1/7 sinB= 5/SQRT74 Find the exact value of tan(A+B).

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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).
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
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%28B%29=5%2Fsqrt%2874%29
cos%28B%29=sqrt%281-sin%5E2%28B%29%29=sqrt%281-25%2F74%29=sqrt%2849%2F74%29=7%2Fsqrt%2874%29
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..