SOLUTION: Find the exact value of cos(a+b) given that cot b = 1/5 and cos a = 12/13 where a is in quadrant I and b is in quadrant III.

Question 772748: Find the exact value of cos(a+b) given that cot b = 1/5 and cos a = 12/13 where a is in quadrant I and b is in quadrant III.
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Find the exact value of cos(a+b) given that cot b = 1/5 and cos a = 12/13 where a is in quadrant I and b is in quadrant III.
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Identity: cos(a+b)=cos a cos b-sin a sin b
..
cos a=12/13
sin a=5/13
..
cot b=1/5=cos b/sin b
hypotenuse=
cos b=
sin b=
cos(a+b)=
cos(a+b)=
cos(a+b)=
..
calculator check:
cot b=1/5
tan b=5
b=78.69�+180�≈258.69�
cos a=12/13
a=22.62�
a+b≈281.31�
cos(a+b)=cos(281.31�)≈0.1961
exact value=≈0.1961
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