Question

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

Answer 1

(d).
`(152)/(377)`

Explanation:

sin² β + cos² β = 1

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

cos α = √(1 -
`(400)/(841)` ) = 21 / 29

cos β = 12 / 13

sin β = √(1 -
`(144)/(169)` ) = 5 / 13

sin α = 20 / 29

cos (α + β) =
`(21)/(29)` ×
`(12)/(13)` -
`(20)/(29)` ×
`(5)/(13)` =
`(152)/(377)`