The general solution of the differential equation `(dy)/(dx)+(1+cos2y)/(1-cos2x)=0` is given by

Options

A. `tan y+cotx=c`
B. `tan y-cotx=c`
C. `tan x-coty=c`
D. `tan x+coty=c`

Answer

B

Explanation

We have , `(dy)/(dx)+(1+cos2y)/(1-cos2x)=0`
`therefore (dy)/(dx)=-(1+cos2y)/(1-cos2x)=-(2cos^2y)/(2sin^2x)`
`1+cosA=2cos^2(A)/(2)`
`1-cosA=2sin^2(A)/(2)`
`rArr int sec^2ydy=-intcosec^2xdx`
`rArr tan y=cot x+C`