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mathlove 13/03/2017 at 18:12
Setting x is the are to find. Easy to see that \(\left(1\right)+\left(2\right)+\left(1\right)=1-\dfrac{\pi}{4}\).
According to the previous post: \(\left(1\right)=1-\dfrac{\sqrt{3}}{4}-\dfrac{\pi}{6}\). So that\(\left(2\right)=\left(1-\dfrac{\pi}{4}\right)-2\left(1-\dfrac{\sqrt{3}}{4}-\dfrac{\pi}{6}\right)=-1+\dfrac{\pi}{12}+\dfrac{\sqrt{3}}{2}\).
Therefore \(x=\dfrac{\pi}{4}-\left[3.\left(2\right)+2.\left(1\right)\right]=\dfrac{\pi}{4}-\left[\left(-3+\dfrac{\pi}{4}+\dfrac{3\sqrt{3}}{2}\right)+\left(2-\dfrac{\sqrt{3}}{2}-\dfrac{\pi}{3}\right)\right]\)
\(=1+\dfrac{\pi}{3}-\sqrt{3}\) .
Selected by MathYouLike -
FA KAKALOTS 28/01/2018 at 22:10
Setting x is the are to find. Easy to see that (1)+(2)+(1)=1−π4.
According to the previous post: (1)=1−√34−π6. So that
(2)=(1−π4)−2(1−√34−π6)=−1+π12+√32
.
Therefore x=π4−[3.(2)+2.(1)]=π4−[(−3+π4+3√32)+(2−√32−π3)]
=1+π3−√3
.