Question

What are the values that satisfy the trigonometric equation for: 0≤q≤2π ?
sin(∅)+tan(−∅)

Answer 1

First choice: 0, pi

Explanation:

I am assuming the equation is

`\sin q + \tan (-q) = 0`

(the =0 part is missing in the original problem)

`\sin q + \tan (-q) = 0\\\sin q + (\sin (-q) )/(\cos (-q)) = 0\\\sin q + (-\sin q)/(\cos q)=0\\\sin q = (\sin q)/(\cos q)\\\sin q \cdot \cos q = \sin q\,\,,\,\,\, 0\leq q \leq 2\pi\\\implies\\\cos q = 1 \implies q=\{0, 2\pi\}\\\mbox{or}\\\sin q = 0 \implies q=\{0, \pi, 2\pi\}\\\implies\\q=\{0,\pi,2\pi\}`

So, the full solution for q is three values: 0, pi, 2pi. This matches the first choice (which is not complete, but that is ok)