Answer:
(d). [tex]\frac{152}{377}[/tex]
Step-by-step explanation:
sin² β + cos² β = 1
cos (α + β) = cos α cos β - sin α sin β
cos α = √(1 - [tex]\frac{400}{841}[/tex] ) = 21 / 29
cos β = 12 / 13
sin β = √(1 - [tex]\frac{144}{169}[/tex] ) = 5 / 13
sin α = 20 / 29
cos (α + β) = [tex]\frac{21}{29}[/tex] × [tex]\frac{12}{13}[/tex] - [tex]\frac{20}{29}[/tex] × [tex]\frac{5}{13}[/tex] = [tex]\frac{152}{377}[/tex]
