Question

Tan x + tan y = 25, cot x+ cot y= 30, find tan (x+y).

Answer 1

tanx + tany = 25
and, cotx +coty = 30
⇒1/tanx +1/tany = 30
⇒(tany +tanx)/tanx tany = 30
⇒25/tanx tany = 30
⇒tanx tany = 5/6

now, tan(x+y) = (tanx+tany)/(1- tanx tany)
                      =25/(1-5/6)
                      =25/(1/6) = 150