б) sin 60° - sin 30°; г) cos 80° - cos 30°; e) sin \(\frac{\pi}{14}\) + sin \(\frac{\pi}{3}\); з) cos \(\frac{\pi}{10}\) + cos \(\frac{\pi}{5}\).

Ответ: смотри решение

б) sin 60° - sin 30° = 2cos((60°+30°)/2)sin((60°-30°)/2) = 2cos45°sin15°

г) cos 80° - cos 30° = -2sin((80°+30°)/2)sin((80°-30°)/2) = -2sin55°sin25°

e) sin \(\frac{\pi}{14}\) + sin \(\frac{\pi}{3}\) = 2sin((\(\frac{\pi}{14}\) + \(\frac{\pi}{3}\))/2)cos((\(\frac{\pi}{14}\) - \(\frac{\pi}{3}\))/2) = 2sin((17π)/84)cos((-11π)/84) = 2sin((17π)/84)cos((11π)/84)

з) cos \(\frac{\pi}{10}\) + cos \(\frac{\pi}{5}\) = 2cos((\(\frac{\pi}{10}\) + \(\frac{\pi}{5}\))/2)cos((\(\frac{\pi}{10}\) - \(\frac{\pi}{5}\))/2) = 2cos((3π)/20)cos((-π)/20) = 2cos((3π)/20)cos((π)/20)

Ответ: б) 2cos45°sin15°; г) -2sin55°sin25°; e) 2sin((17π)/84)cos((11π)/84); з) 2cos((3π)/20)cos((π)/20)