Question

Please solve Tan(3x)=-root3

Answer 1

The question is given below as

`\tan(3x)=-√(3)`

Step 1:

Take the arctan of both sides

`\begin{gathered} \tan(3x)=-√(3) \\ 3x=\tan^(-1)-√(3) \\ \tan^(-1)√(3)=60^0 \\ tan\text{ is \lparen-ve in the second and fourth quadrant\rparen} \\ hence \\ \theta=180-60^0=120^0 \\ \theta=360-60^0=300^0 \\ (3x)/(3)=(120^0)/(3),x=(300)/(3) \\ x=40^0,x=100 \\ x=(2\pi)/(9),x=(5\pi)/(9) \end{gathered}`

Hence,

The values of x are given below as

`x=(2\pi)/(9)+(\pi n)/(3)`

where n could be, 1,2,3,4......