Solution of the differential equation `tan y.sec^(2) x dx + tan x. sec^(2)y dy = 0` is

Options

A. `tan y tan x = C`
B. `(tan y)/(tan x) =C`
C. `(tan^(2)x)/(tan y) = C`
D. None of these

Answer

a

Explanation

Given , ` (sec^(2)x)/(tanx) dx = -(sec^(2)y)/(tany) dy`
On integrating , we get
` rArr int (sec^(2)x)/(tanx) dx =- int (sec^(2)y)/(tany) dy " "` …(i)
Put tan x = u
` rArr sec^(2) x dx = du and tan y = v `
`rArr sec^(2) y dy = dv`
From Eq. (i) ` int (du)/u = - int (du)/v`
` rArr log u = - log v + log C rArr uv = C`
` :. tan x * tany = C`