SOLUTION: Find (Cos a-b) given that Cos a= 5/13 and cos b= 3/5 and that both are between 0 and π/2. Show all work please. Stumped on the identities.

Algebra ->  Trigonometry-basics -> SOLUTION: Find (Cos a-b) given that Cos a= 5/13 and cos b= 3/5 and that both are between 0 and π/2. Show all work please. Stumped on the identities.      Log On


   

Question 777560: Find (Cos a-b) given that Cos a= 5/13 and cos b= 3/5 and that both are between 0 and π/2. Show all work please. Stumped on the identities.
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Find (Cos a-b) given that Cos a= 5/13 and cos b= 3/5 and that both are between 0 and π/2.
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cos(a-b)=cos a*cos b+sin a*sin b
given cos a=5/13
sin a=√(1-cos^2a)=√(1-(25/169))=√(144/169)=12/13
given cos b=3/5
sin b=√(1-cos^2b)=√(1-(9/25))=√(16/25)=4/5
cos(a-b)=5/13*3/5+12/13*4/5=15/65+48/65=63/65