Answer: -56/65
sin α = 4/5 => cos α = 3/5 (because 0 < α < pi/2)
cos β = -12/13 ⇒ sin β = 5/13 (because pi/2 < β < pi)
we have:
cos(α + β) = cosα.cosβ - sinα.sinβ = [tex]\frac{3}{5}.\frac{-12}{13}-\frac{4}{5}.\frac{5}{13}=\frac{-56}{65}[/tex]
Step-by-step explanation:
