Solve the equation `tan^4x+tan^4y+2cot^2xcot^2y=3+sin^2(x+y)` for the values of `x and y dot`

Explanation

`tan^(4) x+tan^(4)y+2 cot^(2) x cot^(2) y=3+sin^(2) (x+y)`
or `tan^(4) x+tan^(4)y+2 cot^(2) x cot^(2) y-2=1+sin^(2) (x+y)`
or `(tan^(2) x-tan^(2) y)^(2) +2(tan x tan y-cot x cot y)^(2)`
`=-1 + sin^(2) (x+y)`
Now `L.H.S. ge 0 and R.H.S. le 0`
`rArr L.H.S.= R.H.S.=0`
`rArr tan^(2) x=tan^(2) y and tan^(2) x tan^(2) y=1`
and `sin^(2) (x+y)=0`
`rArr tan^(2) y=1 and a+y=n pi, n in Z`
`rArr x=mpi pm pi/4, m in Z and y=p pi pm pi/4, p in Z`.