Posted by **House** on Friday, October 3, 2008 at 1:16pm.

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) = 1/5

cos(a) = -2/5

tan(b) = -2/3

opposite side = 2 and adjacentside = 3

hypotenuse = sqrt(4+9) = 13

sin(b) = 2/13

cos(b) = -3/13

cos(a+b) = cosa cosb - sina sinb

=(-2/5)(-3/13) - (1/5)(2/13)

= 6/65 - 2/65

= 4/65

right?

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