9.35 Представьте в виде произведения (9.35—9.37): a) sin 20° + sin 10°; B) cos 70° + cos 20°; д) cos \(\frac{\pi}{5}\) + cos \(\frac{\pi}{4}\); ж) sin \(\frac{\pi}{3}\) - sin \(\frac{\pi}{4}\);

Ответ: смотри решение

a) sin 20° + sin 10° = 2sin((20°+10°)/2)cos((20°-10°)/2) = 2sin15°cos5°

в) cos 70° + cos 20° = 2cos((70°+20°)/2)cos((70°-20°)/2) = 2cos45°cos25°

д) cos \(\frac{\pi}{5}\) + cos \(\frac{\pi}{4}\) = 2cos((\(\frac{\pi}{5}\)+\(\frac{\pi}{4}\))/2)cos((\(\frac{\pi}{5}\)-\(\frac{\pi}{4}\))/2) = 2cos((9π)/40)cos((-π)/40) = 2cos((9π)/40)cos((π)/40)

ж) sin \(\frac{\pi}{3}\) - sin \(\frac{\pi}{4}\) = 2cos((\(\frac{\pi}{3}\)+\(\frac{\pi}{4}\))/2)sin((\(\frac{\pi}{3}\)-\(\frac{\pi}{4}\))/2) = 2cos((7π)/24)sin((π)/24)

Ответ: a) 2sin15°cos5°; в) 2cos45°cos25°; д) 2cos((9π)/40)cos((π)/40); ж) 2cos((7π)/24)sin((π)/24)