Question

How do you solve `Sintheta+ tan(-theta) = 0`?

Answer 1

`f(x) = sin x + sin (-x)/cos (-x) = 0`

or sin (-x) = -sin x, and cos (-x) = cos x, then

`f(x) = (sin x.cos x - sin x)/cos x = 0`

sin x(cos x - 1) = 0

sin x = 0 -> x = 0; x = pi; x = 2pi.

cos x = 1 -> x = 0; x = 2pi.