CPM Homework Help : PC3 Problem 10-115

If $\sin(A) = \frac { 5 } { 13 }$ and $\sec(B) =\frac { 5 } { 4 }$ , where $0 < A, B < \frac { \pi } { 2 }$ , determine the exact value of:

$\cos(A)$

$\sin(B)$

$\cos(A + B)$

Hint:

2 right triangles, first has angle opposite vertical leg labeled, A, hypotenuse labeled 13, vertical leg labeled 5, horizontal leg labeled 12, second has angle opposite vertical leg labeled b, hypotenuse labeled 5, vertical leg labeled 3, horizontal leg labeled 4.

More Help:

$\cos(A + B) = \cos^2(A) − \cos^2(B)$