SOLUTION: a and b are positive acute angles. if sin a= 3/5 and cos b= 12/13, find the value of cos(a-b)

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Question 846190: a and b are positive acute angles. if sin a= 3/5 and cos b= 12/13, find the value of cos(a-b)
Answer by lwsshak3(11628) About Me  (Show Source):
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a and b are positive acute angles. if sin a= 3/5 and cos b= 12/13, find the value of cos(a-b)
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Identity: cos(a-b)=cos a cos b+sin a sin b
..
sin a=3/5
cos a=4/5
cos b=12/13
sin b=5/13
..
cos(a-b)=4/5*12/13+3/5*5/13=48/65+15/65=63/65
..
calculator check:
sin a=3/5
a=36.87˚
..
cos b≈12/13
b≈22.62˚
..
a-b≈14.25˚
..
cos(a-b)≈cos(14.25)≈0.9692
exact ans:
cos(a-b)=63/65≈0.9692