Question

Find the principal solution of the equation. tan x = 1/√3

Answer 1

Answer:

π/6

Step-by-step explanation:

tan x = 1/√3

x = 30°

x = π/6

Answer 2

The principal value of $\tan x=\dfrac{1}{\sqrt{3} }$   is  $\dfrac{\pi}{6}\text{ and } \dfrac{7\pi}{6}$

Step-by-step explanation:

To find: The principal solution of $\tan x=\dfrac{1}{\sqrt{3} }$

as we know he value of tan x is positive in 1st and 3rd quadrant

Now

Let

$\tan x=\dfrac{1}{\sqrt{3} }\\\\\Rightarrow \tan x = tan (\dfrac{\pi}{6} )\\\\\text{if } \tan x = \tan y \text { then } x= y$

Therefore we have

$x= \dfrac{\pi}{6}$

Now tan x is positive in 3rd quadrant

Therefore

$\tan x=\dfrac{1}{\sqrt{3} }\\\\\Rightarrow \tan x = tan (\pi+\dfrac{\pi}{6} )\\\\\text{if } \tan x = \tan y \text { then } x= y$

$\Rightarrow x= \pi+\dfrac{\pi}{6} = \dfrac{7\pi}{6}$

Hence, the principal value of $\tan x=\dfrac{1}{\sqrt{3} }$   is  $\dfrac{\pi}{6}\text{ and } \dfrac{7\pi}{6}$

#Learn  more

Find the principal solution of the equation.

cos x = 1/2

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