Question

sin 3π/14-sin π/14-sin 5π/14=

Answer 1

$sinfrac{3pi}{14}-sinfrac{pi}{14}-sinfrac{5pi}{14}=\\ -2sinfrac{frac{2pi}{14}}{2}*cosfrac{frac{8pi}{14}}{2}-sinfrac{pi}{14} \\ -2sinfrac{pi}{14}*cosfrac{2pi}{7}-sinfrac{pi}{14}=\\ -sinfrac{pi}{14}(2cosfrac{2pi}{7}+1)=\\ frac{ 2cosfrac{pi}{14}* -sinfrac{pi}{14}(2cosfrac{2pi}{7}+1)}{2cosfrac{pi}{14}}=\\ frac{-sinfrac{pi}{7}*(2cosfrac{2pi}{7}+1)}{ 2cosfrac{pi}{14}} =$
теперь заметим что   
  $sinfrac{pi}{7}*2cosfrac{2pi}{7}+sinfrac{pi}{7}=\ cosfrac{pi}{14}-cosfrac{5pi}{14}+sinfrac{pi}{7}=\ cosfrac{5pi}{14}=sinfrac{pi}{7}\ cosfrac{pi}{14}-cosfrac{5pi}{14}+sinfrac{pi}{7}=cosfrac{pi}{14}\\ frac{-cosfrac{pi}{14}}{2cosfrac{pi}{14}}=-frac{1}{2}$