Question

Giai các phương trình sau :

a/ tan 3x = tan x

b/ tan 3x + tan x = 0

c/ tan 2x - tan x = 0

d/ tan 2x + tan x = 0

HELP ME !!!!

Answer 1

a/ \(tan3x=tanx\Rightarrow3x=x+k\pi\Rightarrow2x=k\pi\Rightarrow x=\frac{k\pi}{2}\)

b/ \(tan3x+tanx=0\Rightarrow tan3x=-tanx=tan\left(\pi-x\right)\)

\(\Rightarrow3x=\pi-x+k\pi\Rightarrow4x=\pi+k\pi\Rightarrow x=\frac{\pi}{4}+\frac{k\pi}{4}\)

c/ \(tan2x-tanx=0\Rightarrow tan2x=tanx\)

\(\Rightarrow2x=x+k\pi\Rightarrow x=k\pi\)

d/ \(tan2x+tanx=0\Rightarrow tan2x=-tanx=tan\left(\pi-x\right)\)

\(\Rightarrow2x=\pi-x+k\pi\Rightarrow3x=\pi+k\pi\Rightarrow x=\frac{\pi}{3}+\frac{k\pi}{3}\)