Find the exact value of tan (x+y) if csco = 5/3 and cosy=5/13

-63/16

Step-by-step explanation:

csc x = 5/3

sin x = 3/5

So x is the angle in a 3-4-5 triangle, opposite of the 3.

cos y = 5/13

So y is the angle in a 5-12-13 triangle, opposite of the 12.

tan (x + y) = (tan x + tan y) / (1 - tan x tan y)

tan (x + y) = (3/4 + 12/5) / (1 - (3/4) (12/5))

tan (x + y) = (3/4 + 12/5) / (1 - 9/5)

tan (x + y) = (15 + 48) / (20 - 36)

tan (x + y) = - 63/16