Answer:
[tex]tan\:\left(\frac{5\pi }{6}\right)=tan\left(-\frac{\pi }{6}\right)[/tex]
Option A is correct.
Step-by-step explanation:
We need to find equivalent of [tex]tan\:\left(\frac{5\pi }{6}\right)[/tex]
First we solve [tex]tan\:\left(\frac{5\pi }{6}\right)[/tex]
We get [tex]-\frac{1}{\sqrt{3} }[/tex]
Now checking all the options.
Option A: [tex]tan\:(-\frac{\pi}{6} )[/tex]
Solving [tex]tan\left(-\frac{\pi }{6}\right)\: we\: get\: \mathbf{ -\frac{1}{\sqrt{3} }}[/tex]
Option B: [tex]tan\left(\frac{7\pi }{6}\right)[/tex]
Solving [tex]tan\left(\frac{7\pi }{6}\right)\: we\: get\: \mathbf{\frac{1}{\sqrt{3} }}[/tex]
Option C: [tex]cot\left(\frac{5\pi }{6}\right)[/tex]
Solving [tex]cot\left(\frac{5\pi }{6}\right)\:we\:get\:\mathbf{-\sqrt{3} }[/tex]
Option D : [tex]tan\left(-\frac{5\pi }{6}\right)[/tex]
Solving [tex]tan\left(-\frac{5\pi }{6}\right) \:we\:get:\mathbf{\frac{1}{\sqrt{3} } }[/tex]
So, looking at the options, only Option A has the same result as given question
So, [tex]tan\:\left(\frac{5\pi }{6}\right)=tan\left(-\frac{\pi }{6}\right)[/tex]
Option A is correct.
