Convert the expression
then, multiply the fractions, numerators and denominators separately
and you'll get 10/3, to simplify it'll be 3 1/3 or 3.3333
Answer:
A is spanned by vector.
Step-by-step explanation:
The null space of matrix is set of all solutions to matrix. The linearly independent vectors forms subset which are spanned and forms the null space. The null space of vector can be found by reducing its echelon. The non zero rows formed are the null spaces of matrix.
Answer:
![tan\:\left(\frac{5\pi }{6}\right)=tan\left(-\frac{\pi }{6}\right)](https://tex.z-dn.net/?f=tan%5C%3A%5Cleft%28%5Cfrac%7B5%5Cpi%20%7D%7B6%7D%5Cright%29%3Dtan%5Cleft%28-%5Cfrac%7B%5Cpi%20%7D%7B6%7D%5Cright%29)
Option A is correct.
Step-by-step explanation:
We need to find equivalent of ![tan\:\left(\frac{5\pi }{6}\right)](https://tex.z-dn.net/?f=tan%5C%3A%5Cleft%28%5Cfrac%7B5%5Cpi%20%7D%7B6%7D%5Cright%29)
First we solve ![tan\:\left(\frac{5\pi }{6}\right)](https://tex.z-dn.net/?f=tan%5C%3A%5Cleft%28%5Cfrac%7B5%5Cpi%20%7D%7B6%7D%5Cright%29)
We get ![-\frac{1}{\sqrt{3} }](https://tex.z-dn.net/?f=-%5Cfrac%7B1%7D%7B%5Csqrt%7B3%7D%20%7D)
Now checking all the options.
Option A: ![tan\:(-\frac{\pi}{6} )](https://tex.z-dn.net/?f=tan%5C%3A%28-%5Cfrac%7B%5Cpi%7D%7B6%7D%20%29)
Solving ![tan\left(-\frac{\pi }{6}\right)\: we\: get\: \mathbf{ -\frac{1}{\sqrt{3} }}](https://tex.z-dn.net/?f=tan%5Cleft%28-%5Cfrac%7B%5Cpi%20%7D%7B6%7D%5Cright%29%5C%3A%20we%5C%3A%20get%5C%3A%20%5Cmathbf%7B%20-%5Cfrac%7B1%7D%7B%5Csqrt%7B3%7D%20%7D%7D)
Option B: ![tan\left(\frac{7\pi }{6}\right)](https://tex.z-dn.net/?f=tan%5Cleft%28%5Cfrac%7B7%5Cpi%20%7D%7B6%7D%5Cright%29)
Solving ![tan\left(\frac{7\pi }{6}\right)\: we\: get\: \mathbf{\frac{1}{\sqrt{3} }}](https://tex.z-dn.net/?f=tan%5Cleft%28%5Cfrac%7B7%5Cpi%20%7D%7B6%7D%5Cright%29%5C%3A%20we%5C%3A%20get%5C%3A%20%5Cmathbf%7B%5Cfrac%7B1%7D%7B%5Csqrt%7B3%7D%20%7D%7D)
Option C: ![cot\left(\frac{5\pi }{6}\right)](https://tex.z-dn.net/?f=cot%5Cleft%28%5Cfrac%7B5%5Cpi%20%7D%7B6%7D%5Cright%29)
Solving ![cot\left(\frac{5\pi }{6}\right)\:we\:get\:\mathbf{-\sqrt{3} }](https://tex.z-dn.net/?f=cot%5Cleft%28%5Cfrac%7B5%5Cpi%20%7D%7B6%7D%5Cright%29%5C%3Awe%5C%3Aget%5C%3A%5Cmathbf%7B-%5Csqrt%7B3%7D%20%7D)
Option D : ![tan\left(-\frac{5\pi }{6}\right)](https://tex.z-dn.net/?f=tan%5Cleft%28-%5Cfrac%7B5%5Cpi%20%7D%7B6%7D%5Cright%29)
Solving ![tan\left(-\frac{5\pi }{6}\right) \:we\:get:\mathbf{\frac{1}{\sqrt{3} } }](https://tex.z-dn.net/?f=tan%5Cleft%28-%5Cfrac%7B5%5Cpi%20%7D%7B6%7D%5Cright%29%20%5C%3Awe%5C%3Aget%3A%5Cmathbf%7B%5Cfrac%7B1%7D%7B%5Csqrt%7B3%7D%20%7D%20%7D)
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)](https://tex.z-dn.net/?f=tan%5C%3A%5Cleft%28%5Cfrac%7B5%5Cpi%20%7D%7B6%7D%5Cright%29%3Dtan%5Cleft%28-%5Cfrac%7B%5Cpi%20%7D%7B6%7D%5Cright%29)
Option A is correct.