Given Sin A = ¾ and Cos B= ⅘ find Cos(A+B) - Sin(A+B) if 0<A<pi/2 and 3pi/2<B<2pi

Answer 1

Given Sin A = ¾ and Cos B= ⅘ find Cos(A+B) - Sin(A+B) if 0<A<pi/2 and 3pi/2<B<2pi

Sin^-1(3/4) = A = 48.59° Cos^-1(4/5) = B = 36.87°, but located in the 4th quadrant B is -36.87°

Cos(A+B) = Cos( 48.59 - 36.87) = Cos(11.72) = 0.979

Sin(A+B) = Sin(11,72) = 0.203

Cos(A+B) - Sin(A+B) = 0.979 - 0.203 = 0.776