Question

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

Answer 1

-63/16

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