Answer:
-36/85
Explanation:
We know cos(a)=-8/17, sin (b)=-4/5 to solve the problem we need to find cos(b) and sin(a) since:
Cos(a+b)=cos(a)*cos(b)-sin(a)*sin(b)
To do this, we will use the following relation: sin2(a)+cos2(a)=1
sin2(b)+cos2(b)=1
Using the above equation., we have this:
cos(b) = sqrt( 1 - sin2(b) )= sqrt(1 - 16/25)= 3/5 . the cos(b) is positive since b is in the range (270, 360).
sin(a)= sqrt(1 - cos2(a))= sqrt(1 - 64/289)= -15/17, the sin(a) is negative since a is in the range (180, 270)
Now we can obtain our expression
cos(a+b)=(-8/17)*(3/5) - (-15/17)*(-4/5)= -36/85