Question

Find the value of tan 7π/6....<br /><br />Derive the angle using the identity....tan (2π-x)=-tan x

Answer 1

Tan( 7π/6)=tan(π +π/6)
=Tan(π/6) ,using identity { tan (180 +x)}.
=Tan 30°
=1/√3

Answer 2

Answer:  The answer is $\dfrac{1}{\sqrt 3}.$

Step-by-step explanation:  We are given to find the value of the following trigonometric expression:

$E=\tan \dfrac{7\pi}{6}$.

We have the identity that $\tan(2\pi+x)=\tan x,$ since the angle falls in the first quadrant.

In the first quadrant, the values of all the trigonometric ratios is positive.

We have

$E\\\\=\tan \dfrac{7\pi}{6}\\\\\\=\tan(\pi+\dfrac{\pi}{6})\\\\\\=\tan \dfrac{\pi}{6}\\\\=\tan 30^\circ\\\\=\dfrac{1}{\sqrt 3}.$

Thus, the required value is $\dfrac{1}{\sqrt 3}.$