# Math

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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

= 4/ã65

right?

• Math -

I didn't check all, but you have the technique. You can easily check these on your calculator.

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