Question

tan 2x /3 = root 3 find the general solution ​

Answer 1

2x/3=root 3

2x=root3× 3

2x=3root3

Answer 2

The general solution is $x=2n\pi +(-1)^{2n}\times \dfrac{\pi}{2}$

Step-by-step explanation:

Since we have given that

$\tan \dfrac{2x}{3}=\sqrt{3}$

As we know that

$\tan \dfrac{\pi }{3}=\sqrt{3}$

So, we get that

$\tan \dfrac{2x}{3}=\tan \dfrac{\pi }{3}\\\\\dfrac{2x}{3}=\dfrac{\pi}{3}\\\\x=\dfrac{\pi }{3}\times \dfrac{3}{2}\\\\x=\dfrac{\pi }{2}$

So, the general solution is given by

$x=2n\pi +(-1)^{2n}y\\\\x=2n\pi +(-1)^{2n}\times \dfrac{\pi}{2}$

Hence, the general solution is $x=2n\pi +(-1)^{2n}\times \dfrac{\pi}{2}$