Question

Find the principal solution of the equation.
cot x= √3

Answer 1

Answer:

cot x=√3

tan x= -1/√3

tan x= 150

Tan x =150× π/180

tan x= 5π/6

So, Tan x= nπ +5π/6

Answer 2

As per the data given in the above question.

We have to find the principal solution of the given equation.

Given,

$cot \: x= √3$

Step-by-step explanation:

The given equation is

$cot \: x= √3$

We can write the equation as

$tan \: x = \frac{1}{ \sqrt{3} }$

We know that ,the value of tan x is known

$tan \: \frac{\pi}{6} = \frac{1}{ \sqrt{3} }$

$tan \: x= tan \: \frac{\pi}{6}$

$x = \frac{\pi}{6} \: \: \: \: ...(1)$

and tan x is positive in 3rd quadrant

$tan(π+x)= tan x \: \: \: \: \: \: ...(2)$

Now ,put the value of x in equation (2)

$tan(π+ \frac{\pi}{6} )= tan \: x$

$tan \: x = tan ( \frac{6\pi + \pi}{6} )$

$tan \: x = tan \: \frac{7\pi}{6}$

$x = \frac{7\pi}{6} \: \: \: \: \: \:....... (3)$

Therefore,

$tan \: \frac{\pi}{6} = tan \: \frac{7\pi}{6} = \frac{1}{ \sqrt{3} }$

Hence,

The required principal solution cot √3 i.e. tan 1/√3 are

$x = \frac{\pi}{6} \: and \: x = \frac{7\pi}{6}$

Project code #SPJ3