Question

Answer the question above ​

Answer 1

`tan\:\left((5\pi )/(6)\right)=tan\left(-(\pi )/(6)\right)`

Option A is correct.

Explanation:

We need to find equivalent of
`tan\:\left((5\pi )/(6)\right)`

First we solve
`tan\:\left((5\pi )/(6)\right)`

We get
`-(1)/(√(3) )`

Now checking all the options.

Option A:
`tan\:(-(\pi)/(6) )`

Solving
`tan\left(-(\pi )/(6)\right)\: we\: get\: \mathbf{ -(1)/(√(3) )}`

Option B:
`tan\left((7\pi )/(6)\right)`

Solving
`tan\left((7\pi )/(6)\right)\: we\: get\: \mathbf{(1)/(√(3) )}`

Option C:
`cot\left((5\pi )/(6)\right)`

Solving
`cot\left((5\pi )/(6)\right)\:we\:get\:\mathbf{-√(3) }`

Option D :
`tan\left(-(5\pi )/(6)\right)`

Solving
`tan\left(-(5\pi )/(6)\right) \:we\:get:\mathbf{(1)/(√(3) ) }`

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

So,
`tan\:\left((5\pi )/(6)\right)=tan\left(-(\pi )/(6)\right)`

Option A is correct.