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.
mark me brainliest for no reason :>
If sin(90°) = 1, then cos(90°-90°) = cos(0°) = 1
The interest rate is calculated semiannually which means twice a year so you do 2.4/2 which equals 1.2 so the answer is D