Question

7tanx+3=10tanx Identify all possible solutions.

Answer 1

`\huge\boxed{x=(\pi)/(4)+k\pi,\ k\in\mathbb{Z}}\\.\qquad\qquad\downarrow\\\huge\boxed{x=45^o+k\pi,\ k\in\mathbb{Z}}`

Explanation:

`10\tan x=7\tan x+3\qquad\text{subtract}\ 7\tan x\ \text{from both sides}\\\\10\tan x-7\tan x=7\tan x-7\tan x+3\\\\3\tan x=3\qquad\text{divide both sides by 3}\\\\(3\tan x)/(3)=(3)/(3)\\\\\tan x=1\Rightarrow\ x=(\pi)/(4)+k\pi,\ k\in\mathbb{Z}`