Given csc A = - 53 and cot B = 512 32 <A< 2π and π<B< 32 find cos(A + B)

Answer 1

If you could provide some clarity to the comments above I suggest the following

Use the identities

sin(A + B) = SinAcosB + cosAsinB

Use the relationship between the csc and the sin

Use the relationship between the cot, tan, and cos;

cot B = 5/12 this represents the cos/sin both of which are ratios over the hypotenuse, that you can find using the Pythagorean Theorem.

Use the numbers given in the ratios to label the sides of your right triangles

Use the boundaries/limitations to determine what quadrants your right triangles are in