Question

Use the given information to evaluate cos(alpha+beta).

sin alpha= -7/25, cot beta= -8/15; neither alpha nor beta are in quadrant IV

Answer 1

First use the sin^2alfa + cos^2alfa = 1 to find the value of cos(alfa).

Answer 2

so we get 49/625 + cos^2(alfa) = 1. right ?

Answer 3

here use formula of cos(a + b) = cosa cosb - sina sinb

Answer 4

\[\cos \left(\sin ^{-1}\left(-\frac{7}{25}\right)+\cot ^{-1}\left(-\frac{8}{15}\right)\right)=\frac{87}{425}=0.204706 \]