Question

Tan x = 3Cot x . Find the value of x.

Answer 1

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Answer 2

Given :

Tan x = 3Cot x

To Find:

Find the value of x.

Solution:

We are given that Tan x = 3Cot x

Now we are supposed to find the value of x

So,tan x - 3 cot x=0

we know that $Cot x = \frac{1}{Tan x}$

So$tan x - \frac{3}{tanx}=0$

$\frac{tan^2x-3}{tan x}=0\\tan^2 x-3=0\\tan^2 x=3\\tan x =\pm \sqrt{3}$

When$tan x = \sqrt{3}$

$x = tan^{-1} \sqrt{3}\\x = \frac{\pi}{3}$

When$tan x = -\sqrt{3}$

We know that $tan(\pi -x)=- tanx$

So,$tan(\pi-\frac{\pi}{3})=-tan \frac{\pi}{3}\\tan(\frac{2\pi}{3})= -\sqrt{3}$

So, $x = \frac{2\pi}{3}$

Hence the value of x is  $\frac{2\pi}{3}$or $\frac{\pi}{3}$