## miley28 what is the value of tan(15/2)?? ..plz help! one year ago one year ago

1. Goten77

|dw:1359868581635:dw| i havent dont this for a while but like.... tan(15/2) would get some random number if thats what it wants and or

2. miley28

the ans is $2\sqrt{2}-(1+\sqrt{3})/\sqrt{3}-1$

3. miley28

but i need an xplanation for this ans please...

4. miley28

sorry it is actually whole divided by$(\sqrt{3}-1)$

5. enka

we can obtain value $$\tan 15$$ from $\tan(45-30)=\frac{\tan45-\tan30}{1+\tan45\tan30} = \frac{1-\frac{1}{\sqrt{3}}}{1+\frac{1}{\sqrt{3}}}=\frac{\sqrt{3}-1}{\sqrt{3}+1}=2-\sqrt{3}$ now, to obtain $$\tan7.5$$ we use $\tan15=\frac{2\tan7.5}{1-\tan^27.5}$ which can solve by Quadratic formula

6. miley28

^ thnku so much..