trig  identies
posted by Anonymous .
Assume that A and B are in standard position and that sin A = 1/2, cos A >0, tan B = 3/4, and sinB<0
Cos (AB)

from sin A = 1/2, cos A >0, we know that A has to be in quadrant I, so cosA = √3/2
from tan B = 3/4, and sinB<0, we know that B must be in quadrante III, so sinB=3/5 and cosB = 4/5
Cos(AB) = cosAcosB + sinAsinB
= √3/2(4/5) + 1/2(3/5)
= (4√3  3)/10