Question

if a and b are two angles in Quadrant II such that tan a = -1/2 and tan B = -2/3 find cos(a+b)

Answer 1

You can use the mother equation to derive cos(a+b)=cos(a)cos(b)-sin(a)sin(b)



-3/2sin(b) = cos(b)
-2sin(a) = cos(a)

cos(a+b) = 3sin(a)sin(b)-1/3cos(a)cos(b) take your pick
= 3/2cos(a)(2/3cos(b))-1/3cos(a)cos(b)
= 2/3cos(a)cos(b)