posted by House on .
If a and B are two angles in Quadrant 2 such that tan a=-1/2 and tan B= -2/3, find cos(a+b)?
tan(a) = -1/2
oppsite side = 1: adjacentside = 2
hypotenuse = sqrt(1+4) = sqrt(5)
sin(a) = 1/ã5
cos(a) = -2/ã5
tan(b) = -2/3
opposite side = 2 and adjacentside = 3
hypotenuse = sqrt(4+9) = ã13
sin(b) = 2/ã13
cos(b) = -3/ã13
cos(a+b) = cosa cosb - sina sinb
=(-2/ã5)(-3/ã13) - (1/ã5)(2/ã13)
= 6/ã65 - 2/ã65
I didn't check all, but you have the technique. You can easily check these on your calculator.