Question

tan x + tan 2x = 0
Is that way is right or wrong for find general solution in trigonometry?
tan x + tan 2x = 0
tan x = - tan 2x
tan x= tan (π - 2x)
x=nπ/3 + π/3 ​

Answer 1

stated method in question is wrong!

Step-by-step explanation:

We need to find the general solution of x ! for the equation $tan x + tan 2x = 0$

⇒  $tan x + tan 2x = 0$

⇒  $(tan x + tan 2x)-tan2x = 0-tan2x$

⇒  $tan x = -tan2x$

Now , we know that $tan(\pi -2x) = -tan2x$

⇒  $tan x = -tan2x$

⇒  $tan x = tan(\pi -2x)$

Now , we know that $TanA = TanB \\A=B$

⇒  $tan x = tan(\pi -2x)$

⇒  $x = \pi -2x$

⇒  $3x = \pi$

⇒  $x = \frac{\pi}{3}$     ......(1)

General solution of Tan x is : $x = n\pi + \alpha$ , \

Here , from equation (1) we get  $\alpha =\frac{\pi }{3}$ . Hence general solution is :

⇒ $x = n\pi +\frac{\pi }{3}$ .Therefore , stated method in question is wrong!