Question

Someone please help me! Studying for finals and don’t understand how to complete problems like this! Thank you!

Answer 1

Answer:

(d). $\frac{152}{377}$

Step-by-step explanation:

sin² β + cos² β = 1

cos (α + β) = cos α cos β - sin α sin β

cos α = √(1 - $\frac{400}{841}$ ) = 21 / 29

cos β = 12 / 13

sin β = √(1 - $\frac{144}{169}$ ) = 5 / 13

sin α = 20 / 29

cos (α + β) = $\frac{21}{29}$ × $\frac{12}{13}$ - $\frac{20}{29}$ × $\frac{5}{13}$ = $\frac{152}{377}$