Question

Answer the question above ​

Answer 1

Answer:

$tan\:\left(\frac{5\pi }{6}\right)=tan\left(-\frac{\pi }{6}\right)$

Option A is correct.

Step-by-step explanation:

We need to find equivalent of $tan\:\left(\frac{5\pi }{6}\right)$

First we solve $tan\:\left(\frac{5\pi }{6}\right)$

We get $-\frac{1}{\sqrt{3} }$

Now checking all the options.

Option A: $tan\:(-\frac{\pi}{6} )$

Solving $tan\left(-\frac{\pi }{6}\right)\: we\: get\: \mathbf{ -\frac{1}{\sqrt{3} }}$

Option B: $tan\left(\frac{7\pi }{6}\right)$

Solving $tan\left(\frac{7\pi }{6}\right)\: we\: get\: \mathbf{\frac{1}{\sqrt{3} }}$

Option C: $cot\left(\frac{5\pi }{6}\right)$

Solving $cot\left(\frac{5\pi }{6}\right)\:we\:get\:\mathbf{-\sqrt{3} }$

Option D : $tan\left(-\frac{5\pi }{6}\right)$

Solving $tan\left(-\frac{5\pi }{6}\right) \:we\:get:\mathbf{\frac{1}{\sqrt{3} } }$

So, looking at the options, only Option A has the same result as given question

So, $tan\:\left(\frac{5\pi }{6}\right)=tan\left(-\frac{\pi }{6}\right)$

Option A is correct.