Trigonometry Equation

Find tan(x-y) if sin(x) = 1/5, cos(y) = 2/5, tan(x) < 0 tan(y) > 0

Solution

In the triangle containing x the remaining side is -2sqrt(6) and in the triangle containing y the remaining side is sqrt(21).

Therefore tan x = -sqrt(6)/12 and tan y =sqrt(21)/2

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

You plug in the values to get the answer!