Solve `(tan^(2) x+2sqrt(3) tan x+7) (cot^(2) y-2 sqrt(3) cot y+8) le 20` for x and y.
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We have `((tan x + sqrt(3))^(2)+4)((cot y-sqrt(3))^(2)+5) le 20` Now, `L.H.S. ge 20`. Therefore, we must have `(tan x+sqrt(3))^(2)=0 and (cot y-sqrt(3))^(2)=0` `rArr tan x=-sqrt(3) and cot y=sqrt(3)` `rArr tan x=-sqrt(3) and tan y=1/sqrt(3)` `rArr x=n pi-pi/3, n in Z` and `y=mpi+pi/6, m in Z`
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