SOLUTION: a and b are quadrant I angles with cos(a)= 15/17 and csc(b) = 41/9. find tan(a-b). a. 37/120 b. 91/120 c. 185/672 d. 455/528 Thanks for your help!

Algebra ->  Trigonometry-basics -> SOLUTION: a and b are quadrant I angles with cos(a)= 15/17 and csc(b) = 41/9. find tan(a-b). a. 37/120 b. 91/120 c. 185/672 d. 455/528 Thanks for your help!      Log On


   

Question 850301: a and b are quadrant I angles with cos(a)= 15/17 and csc(b) = 41/9. find tan(a-b).
a. 37/120 b. 91/120 c. 185/672 d. 455/528
Thanks for your help!
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
a and b are quadrant I angles with cos(a)= 15/17 and csc(b) = 41/9. find tan(a-b).
Identity: tan%28a-b%29=%28tana-tanb%29%2F%281%2Btana%2Atanb%29
cosa=15/17

tana=sin/cos=8/15
..
csc(b)=41/9
sin(b)=9/41

tanb=sin/cos=9/40
..
tan%28a-b%29=%288%2F15-9%2F40%29%2F%281%2B8%2F15%2A9%2F40%29=185%2F672
calculator check:
cos(a)=15/17
a≈28.072˚
sin(b)=9/41
b=12.680
a-b=15.392
tan(a-b)=tan(15.392)≈0.279
exact value=185/672≈0.279 (ans c.)