Evaluate the expression under the given conditions.

Question

sin (A+B); tan A= 12/5, A in quadrant 3, sin B= -3sqrt(10)/10, B in quadrant 4.

Answer 1

in QIII, sin and cos are both negative.
You have a 5-12-13 triangle, so
sinA = -12/13
cosA = -5/13

in QIV, cos is positive.
You have a 3-1-√10 triangle, so
cosB = 1/√10

Now apply the addition formula

sin(A+B) = sinAcosB + cosAsinB