Question

Sin7пи/5-sin17пи/10 помогитее

Answer 1

$sin frac{7 pi }{5} -sinfrac{17 pi }{10}= sin frac{5 pi +2pi}{5} -sinfrac{20 pi-3pi }{10}= \ \ =sin (pi +frac{2pi}{5}) -sin(2pi -frac{3pi }{10})= -sinfrac{2pi}{5}-(-sinfrac{3pi }{10}))= \ \ =sinfrac{3pi }{10}-sinfrac{2pi}{5}=2sin frac{frac{3pi }{10}-frac{2pi}{5}}{2} cosfrac{frac{3pi }{10}+frac{2pi}{5}}{2}=2sin frac{-pi}{20}cos frac{7pi}{20}= \ \ =-2 sin frac{pi}{20}cos frac{7pi}{20}$