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1) умножим и разделим на
, применим формулу синуса двойного угла
![frac{16cos frac{ pi }{9}cos frac{2 pi }{9} cos frac{4 pi }{9 }cdot sin frac{ pi }{9} }{sin frac{ pi }{9} } = \ \ frac{8(2sin frac{ pi }{9} cos frac{ pi }{9})cos frac{2 pi }{9} cos frac{4 pi }{9 } }{sin frac{ pi }{9} } = \ \ frac{8(sin frac{ 2pi }{9})cos frac{2 pi }{9} cos frac{4 pi }{9 } }{sin frac{ pi }{9} } = frac{16cos frac{ pi }{9}cos frac{2 pi }{9} cos frac{4 pi }{9 }cdot sin frac{ pi }{9} }{sin frac{ pi }{9} } = \ \ frac{8(2sin frac{ pi }{9} cos frac{ pi }{9})cos frac{2 pi }{9} cos frac{4 pi }{9 } }{sin frac{ pi }{9} } = \ \ frac{8(sin frac{ 2pi }{9})cos frac{2 pi }{9} cos frac{4 pi }{9 } }{sin frac{ pi }{9} } =](https://tex.z-dn.net/?f=+frac%7B16cos+frac%7B+pi+%7D%7B9%7Dcos+frac%7B2+pi+%7D%7B9%7D+cos+frac%7B4+pi+%7D%7B9+%7Dcdot+sin+frac%7B+pi+%7D%7B9%7D+%7D%7Bsin+frac%7B+pi+%7D%7B9%7D+%7D+%3D+%5C++%5C++frac%7B8%282sin+frac%7B++pi++%7D%7B9%7D+cos+frac%7B+pi+%7D%7B9%7D%29cos+frac%7B2+pi+%7D%7B9%7D+cos+frac%7B4+pi+%7D%7B9+%7D+%7D%7Bsin+frac%7B+pi+%7D%7B9%7D+%7D+%3D+%5C++%5C++frac%7B8%28sin+frac%7B++2pi++%7D%7B9%7D%29cos+frac%7B2+pi+%7D%7B9%7D+cos+frac%7B4+pi+%7D%7B9+%7D+%7D%7Bsin+frac%7B+pi+%7D%7B9%7D+%7D+%3D+++)
![frac{4(2sin frac{ 2pi }{9}cos frac{2 pi }{9} )cos frac{4 pi }{9 } }{sin frac{ pi }{9} } = \ \ = frac{4(sin frac{ 4pi }{9} )cos frac{4 pi }{9 } }{sin frac{ pi }{9} } = \ \ =frac{2(2sin frac{ 4pi }{9} cos frac{4 pi }{9 }) }{sin frac{ pi }{9} } = \ \ =frac{2(sin frac{ 8pi }{9} ) }{sin frac{ pi }{9} } = \ \ =frac{2(sin frac{ pi }{9} ) }{sin frac{ pi }{9} } =2 frac{4(2sin frac{ 2pi }{9}cos frac{2 pi }{9} )cos frac{4 pi }{9 } }{sin frac{ pi }{9} } = \ \ = frac{4(sin frac{ 4pi }{9} )cos frac{4 pi }{9 } }{sin frac{ pi }{9} } = \ \ =frac{2(2sin frac{ 4pi }{9} cos frac{4 pi }{9 }) }{sin frac{ pi }{9} } = \ \ =frac{2(sin frac{ 8pi }{9} ) }{sin frac{ pi }{9} } = \ \ =frac{2(sin frac{ pi }{9} ) }{sin frac{ pi }{9} } =2](https://tex.z-dn.net/?f=+frac%7B4%282sin+frac%7B++2pi++%7D%7B9%7Dcos+frac%7B2+pi+%7D%7B9%7D+%29cos+frac%7B4+pi+%7D%7B9+%7D+%7D%7Bsin+frac%7B+pi+%7D%7B9%7D+%7D+%3D+%5C++%5C+%3D+frac%7B4%28sin+frac%7B++4pi++%7D%7B9%7D+%29cos+frac%7B4+pi+%7D%7B9+%7D+%7D%7Bsin+frac%7B+pi+%7D%7B9%7D+%7D+%3D++%5C++%5C+%3Dfrac%7B2%282sin+frac%7B++4pi++%7D%7B9%7D+cos+frac%7B4+pi+%7D%7B9+%7D%29+%7D%7Bsin+frac%7B+pi+%7D%7B9%7D+%7D+%3D++%5C++%5C+%3Dfrac%7B2%28sin+frac%7B++8pi++%7D%7B9%7D+%29+%7D%7Bsin+frac%7B+pi+%7D%7B9%7D+%7D+%3D++%5C++%5C+%3Dfrac%7B2%28sin+frac%7B++pi++%7D%7B9%7D+%29+%7D%7Bsin+frac%7B+pi+%7D%7B9%7D+%7D+%3D2)
2)умножим и разделим на![cos frac{ pi }{14} cos frac{ pi }{14}](https://tex.z-dn.net/?f=cos+frac%7B+pi+%7D%7B14%7D+)
![frac{(sin frac{3 pi }{14} -sin frac{ pi }{14} -sin frac{5 pi }{14} )cos frac{ pi }{14} }{cos frac{ pi }{14} }= \ \ frac{(sin frac{3 pi }{14}cos frac{ pi }{14}) -(sin frac{ pi }{14}cos frac{ pi }{14}) -(sin frac{5 pi }{14} cos frac{ pi }{14}) }{cos frac{ pi }{14} }= \ \ = frac{(2sin frac{3 pi }{14}cos frac{ pi }{14}) -(2sin frac{ pi }{14}cos frac{ pi }{14}) -(2sin frac{5 pi }{14} cos frac{ pi }{14}) }{2cos frac{ pi }{14} }= frac{(sin frac{3 pi }{14} -sin frac{ pi }{14} -sin frac{5 pi }{14} )cos frac{ pi }{14} }{cos frac{ pi }{14} }= \ \ frac{(sin frac{3 pi }{14}cos frac{ pi }{14}) -(sin frac{ pi }{14}cos frac{ pi }{14}) -(sin frac{5 pi }{14} cos frac{ pi }{14}) }{cos frac{ pi }{14} }= \ \ = frac{(2sin frac{3 pi }{14}cos frac{ pi }{14}) -(2sin frac{ pi }{14}cos frac{ pi }{14}) -(2sin frac{5 pi }{14} cos frac{ pi }{14}) }{2cos frac{ pi }{14} }=](https://tex.z-dn.net/?f=+frac%7B%28sin+frac%7B3+pi+%7D%7B14%7D+-sin+frac%7B+pi+%7D%7B14%7D+-sin+frac%7B5+pi+%7D%7B14%7D+%29cos+frac%7B+pi+%7D%7B14%7D+%7D%7Bcos+frac%7B+pi+%7D%7B14%7D+%7D%3D+%5C++%5C++frac%7B%28sin+frac%7B3+pi+%7D%7B14%7Dcos+frac%7B+pi+%7D%7B14%7D%29++-%28sin+frac%7B+pi+%7D%7B14%7Dcos+frac%7B+pi+%7D%7B14%7D%29++-%28sin+frac%7B5+pi+%7D%7B14%7D+cos+frac%7B+pi+%7D%7B14%7D%29+%7D%7Bcos+frac%7B+pi+%7D%7B14%7D+%7D%3D+%5C++%5C+%3D++frac%7B%282sin+frac%7B3+pi+%7D%7B14%7Dcos+frac%7B+pi+%7D%7B14%7D%29++-%282sin+frac%7B+pi+%7D%7B14%7Dcos+frac%7B+pi+%7D%7B14%7D%29++-%282sin+frac%7B5+pi+%7D%7B14%7D+cos+frac%7B+pi+%7D%7B14%7D%29+%7D%7B2cos+frac%7B+pi+%7D%7B14%7D+%7D%3D)
![frac{(sin frac{4pi }{14}+sin frac{ 2pi }{14}) -sin frac{ 2pi }{14} -(sinfrac{6 pi }{14}+ sin frac{ 4pi }{14}) }{2cos frac{ pi }{14} }= \ \= frac{sin frac{4pi }{14} -sinfrac{6 pi }{14}-sin frac{ 4pi }{14} }{2cos frac{ pi }{14} }= frac{(sin frac{4pi }{14}+sin frac{ 2pi }{14}) -sin frac{ 2pi }{14} -(sinfrac{6 pi }{14}+ sin frac{ 4pi }{14}) }{2cos frac{ pi }{14} }= \ \= frac{sin frac{4pi }{14} -sinfrac{6 pi }{14}-sin frac{ 4pi }{14} }{2cos frac{ pi }{14} }=](https://tex.z-dn.net/?f=frac%7B%28sin+frac%7B4pi+%7D%7B14%7D%2Bsin+frac%7B+2pi+%7D%7B14%7D%29++-sin+frac%7B+2pi+%7D%7B14%7D++-%28sinfrac%7B6+pi+%7D%7B14%7D%2B+sin+frac%7B+4pi+%7D%7B14%7D%29+%7D%7B2cos+frac%7B+pi+%7D%7B14%7D+%7D%3D+%5C++%5C%3D+frac%7Bsin+frac%7B4pi+%7D%7B14%7D++-sinfrac%7B6+pi+%7D%7B14%7D-sin+frac%7B+4pi+%7D%7B14%7D+%7D%7B2cos+frac%7B+pi+%7D%7B14%7D+%7D%3D)
![= frac{ -sinfrac{6 pi }{14} }{2cos frac{ pi }{14} }= frac{ -sin( frac{ pi }{2} -frac{pi }{14} )}{2cos frac{ pi }{14} }= \ \ =-frac{ -cos( frac{pi }{14} )}{2cos frac{ pi }{14} }=- frac{1}{2} = frac{ -sinfrac{6 pi }{14} }{2cos frac{ pi }{14} }= frac{ -sin( frac{ pi }{2} -frac{pi }{14} )}{2cos frac{ pi }{14} }= \ \ =-frac{ -cos( frac{pi }{14} )}{2cos frac{ pi }{14} }=- frac{1}{2}](https://tex.z-dn.net/?f=%3D+frac%7B+-sinfrac%7B6+pi+%7D%7B14%7D+%7D%7B2cos+frac%7B+pi+%7D%7B14%7D+%7D%3D+frac%7B+-sin%28+frac%7B+pi+%7D%7B2%7D+-frac%7Bpi+%7D%7B14%7D+%29%7D%7B2cos+frac%7B+pi+%7D%7B14%7D+%7D%3D+%5C++%5C+%3D-frac%7B+-cos%28+frac%7Bpi+%7D%7B14%7D+%29%7D%7B2cos+frac%7B+pi+%7D%7B14%7D+%7D%3D-+frac%7B1%7D%7B2%7D+)
2)умножим и разделим на
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