SOLUTION: For positive acute angles A and B,, it is known that sin A=9/41 and cos B=3/5 ​ Find the value of cos (A-B) in simplest form. I know that sin A =9/41, 40/41 by drawing a tr

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Question 1193960: For positive acute angles A and B,, it is known that sin A=9/41 and cos B=3/5
​
Find the value of cos (A-B) in simplest form. I know that sin A =9/41, 40/41 by drawing a triangle for help me to understand how to set up.
Robbin
Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(52805)   (Show Source): You can put this solution on YOUR website!
.

Find many similar solved problems of this type in the lesson
    - Evaluating trigonometric expressions
in this site.

Consider them as your TEMPLATES and solve your problem in the same way.

Learn the subject and the solution method from there.



Answer by MathTherapy(10553)   (Show Source): You can put this solution on YOUR website!

For positive acute angles A and B,, it is known that sin A=9/41 and cos B=3/5
​
Find the value of cos (A-B) in simplest form. I know that sin A =9/41, 40/41 by drawing a triangle for help me to understand how to set up.
Robbin
cos (A - B) = cos A cos B + sin A sin B

Based on the above, you'll need cos A and sin B, since cos B and sin A were given.

          As  we can see that x, or the adjacent (A) side MUST be 40 since this is a 9-40-41 Pythagorean Triple. 
We then get: 

          As  we can see that y, or the opposite (O) side MUST be 4 since this is a 3-4-5 Pythagorean Triple. 
We then get:

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