Suppose x and y real number such that `tan x tan y=42 and cot x +cot =49` the value of `tan (x+y)` is ____________

Answer

294

Explanation

`cot x + coty = 49`
or ` (1)/( tan x ) + (1)/( tan y ) = 49`
or `( tan y + tanx)/(tanx tan y )= 49`
or `tan x tany = ( tan x + tan y )/(49) = (42)/(49) = (6)/(7)`
`therefore tan(x+y) = (42)/(1-(6//7)) = (42)/(1//7) = 294`