Answer:
cos (A + B) = - 57 / 185
Explanation:
First we draw the triangle containing angle A
From the above, we find that the length of the hypotenuse is 5; therefore,
[tex]\begin{gathered} \sin A=\frac{3}{5} \\ \cos A=\frac{4}{5} \end{gathered}[/tex]
Now we draw the triangle containing angle B.
The length of the vertical side from Pythagoras's theorem is 35; therefore,
[tex]\sin B=\frac{35}{37}[/tex]
Now,
[tex]\cos A+B=\cos A\cos B-\sin A\sin B[/tex]
Putting in the values of cos A, cos B, sin A, and sin B we found above gives
[tex]\cos A+B=(\frac{4}{5})(\frac{12}{37})-(\frac{3}{5})(\frac{35}{37})[/tex][tex]\boxed{\cos A+B=-\frac{57}{185}}[/tex]
which is our answer!
