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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-> 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(52803) (Show Source):
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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:
