Find all solutions of the equation below. sin𝑥tan𝑥+sin𝑥 =0

Question

Please help me with this problem. I am very lost :/

Answer 1

(sinx)tanx + sinx = 0 or sinx(tanx + 1) = 0

So, the expression = 0 when either sinx = 0 or when tanx + 1 = 0

from 0 to 2pi, sinx is zero when the angle is 0^o or 180^o (and pi multiples)

and when tanx = -1 results when the tanx is negative (+sinx & -cosx or -sinx & +cosx )

This occurs in the 2nd and 4th quadrant when the angle is 135^o and 315^o. (and pi multiples)