Question

Доказать равенство

sin(3pi/10)-sin(pi/10) = 1/2

Answer 1

sin(3pi/10)-sin(pi/10)=sin54°-sin18°=$2sin\frac{54^0-18^0}{2}cos\frac{54^0+18^0}{2} =2sin18^0cos36^0=\frac{2sin18^0cos18^0cos36^0}{cos18^0}= \frac{sin36^0cos18^0cos36^0}{cos18^0}=\frac{2sin36^0cos18^0cos36^0}{2cos18^0}=\frac{sin72^0}{2cos18^0}=\frac{cos18^0}{2cos18^0}=\frac{1}{2}$