You are given that , with A in Quadrant IV, and , with B in Quadrant III. Find cos(A+B). Give your answer as a fraction

-

Step-by-step explanation:

Using the addition formula for cosine

cos(A + B) = cosAcosB - sinAsinB

Given sin A = - = and in fourth quadrant, then

the triangle is a 7 - 24- 25 right triangle with adjacent side 24

In fourth quadrant cosine ratio is positive , thus

cos A = =

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Given sin B = - = and in third quadrant, then

the triangle is a 5- 12- 13 right triangle with adjacent side 5

In third quadrant cosine ratio is negative, thus

cos B = = -

Thus

cosAcosB - sinAsinB

= ( × - ) - (- × - )

= - -

= -

step-by-step explanation: