Finding Exact Value of d tan (π/12)

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The discussion focuses on finding the exact value of d tan(π/12) using compound angle formulas. Participants are encouraged to clarify what "d" refers to and to specify the compound angle formulas being used. Key hints provided include the sine identity involving π/6 and the definition of tan(π/12) in terms of sine and cosine. The conversation emphasizes the need for precise mathematical expressions and calculations. Overall, the goal is to derive the exact value through these mathematical principles.
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Use the compound angle formulas and appropriate angles to find the exact value of each
of the following:
D. d tan (pi/12)

thank you
 
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rachael said:
Use the compound angle formulas and appropriate angles to find the exact value of each
of the following:
D. d tan (pi/12)

thank you

Alright, what have you done? In particular what are the "compound angle formulas" and what is "d"?
 
Hints:

1.\sin \frac{\pi}{6} = 2\sin \frac{\pi}{12} \cos \frac{\pi}{12}

2.\tan \frac{\pi}{12}=\frac{\sin\frac{\pi}{12}}{\cos\frac{\pi}{12}}

Daniel.
 
I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
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