SOLUTION: Find cos(alpha - beta). Alpha and Beta are quadrant 1 angles with cos(alpha)=15/17 and csc(beta)=41/9

Algebra ->  Trigonometry-basics -> SOLUTION: Find cos(alpha - beta). Alpha and Beta are quadrant 1 angles with cos(alpha)=15/17 and csc(beta)=41/9      Log On


   

Question 972693: Find cos(alpha - beta). Alpha and Beta are quadrant 1 angles with cos(alpha)=15/17 and csc(beta)=41/9
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Find cos(alpha - beta). Alpha and Beta are quadrant 1 angles with cos(alpha)=15/17 and csc(beta)=41/9
***
cos a=15/17
sin a=√(1-cos^2(a))=√(1-225/289)=√(64/289)=8/17
..
csc b=41/9
sin b=1/csc b=9/41
cos b=√(1-sin^2(b))=√(1-81/1681)=√(1600/1681)=40/41
...
cos(a+b)=cos a cos b-sin a sin b=15/17*40/41-8/17*9/41=600/697-72/697=528/697
Check:
cos a=15/17
a≈28.07˚
cos b=40/41
b≈12.68˚
a+b≈28.07+12.68
a+b≈40.75˚
cos(a+b)≈cos(40.75)≈0.7575
Exact value as computed=528/697≈0.7575