Answer:
812/1037
Explanation:
To solve this, we have to use trigonometric identities.
Cos (A + B) is given as Cos A Cos B - Sin A Sin B. And from the question, we have that
Tan A = 8/15.
We know that in a triangle, the Tan angle is represented Opp/Adj and thus the Opp is 8, and the Adj is 15. Using Pythagoras, we have
hyp² = opp² + adj²
hyp² = 8² + 15²
hyp² = 64 + 225
hyp² = 289
hyp = √289 = 17
The identity of Cos is Adj/Hyp and that of Sin is Opp/Hyp.
Cos A = 15/17
Sin A = 8/17
Repeating the same process for B, we have
Sin B = 11/61
adj² = hyp² - opp²
adj² = 61² - 11²
adj² = 3721 - 121
adj² = 3600
adj = √3600 = 60
Cos B = 60/61
Now, using the earlier stated trigonometric identity, we have
cos (a + b) = CosA CosB - SinA SinB
cos (a + b) = 15/17 * 60/61 - 8/17 * 11/61
cos (a + b) = 900/1037 - 88/1037
cos (a + b) = 812/1037