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 ofZ.

look at the graph