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.

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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) About Me  (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=sqrt%281%2B5%5E2%29=sqrt%2826%29
cos b=-1%2Fsqrt%2826%29=-sqrt%2826%29%2F26
sin b=-5%2Fsqrt%2826%29=-5sqrt%2826%29%2F26
cos(a+b)=%2812%2F13%29%2A%28-sqrt%2826%29%2F26%29-%285%2F13%29%2A%28-5sqrt%2826%29%2F26%29
cos(a+b)=%28-12%2Asqrt%2826%29%2F338%29%2B%2825%2Asqrt%2826%29%2F338%29
cos(a+b)=13sqrt%2826%29%2F338%29
..
calculator check:
cot b=1/5
tan b=5
b=78.69º+180º≈258.69º
cos a=12/13
a=22.62º
a+b≈281.31º
cos(a+b)=cos(281.31º)≈0.1961
exact value=13sqrt%2826%29%2F338%29≈0.1961