ah, you mean trigonometric equation?
(1+tan(x)) / sin(x) = 0.
cross multiplying, 1 + tan x = 0
tan x = -1
x = arctan (-1)
x = -45 degrees = pi/4 radians
or if u want a family of solutions, x = (pi/4)(4k - 1), where k is an element of Z.
look at the graph