Question

Chapter: General Solutions of Trigonometric Equations

Please solve it .

Answer 1

First we need to know $Tan(a+b)=Tan(a)-Tan(b)/1-tana*tanb$
So tanx + tan2x+tanx*tan2x=1
So tanx + tan2x =1-tanx*tan2x
$Tanx+tan2x/1-tanx * Tan2x$
So by formula above Tan(x+2x)=1
Tan(3x)=1
we know Tan$\pi$/4=1
So Tan3x=Tan($\pi$/4)
So 3x=(4n+1)$\pi$/4
Therefore, x=(4n+1)$\pi$/12