Question

Докажите равенство sin200+sin100=sin40

Answer 1

Решение во вложении,надеюсь поймешь)

Answer 2

$sin200+sin100=sin40\\ 2sin100cos100+sin100=sin100(2cosa100+1)\\ sin(60+40)(2cos(60+40)+1)\\ (frac{sqrt{3}*cos40+sin40}{2})(cos40-sqrt{3}sin40+1)\\ frac{-2cos40sin40+sqrt{3}*cos40+sqrt{3}*cos^240+sin40-sqrt{3}*sin^240}{2}\\ frac{-2cos40sin40+sqrt{3}cos40+sqrt{3}*cos80+sin40}{2}\\ frac{-2cos40sin40+sqrt{3}(cos40+cos80)+sin40}{2}\\ frac{-2cos40*2sin20*cos20+sqrt{3}cos(20)}{2}\\ frac{cos20(-4cos40*sin20+sqrt{3})+sin40}{2}\\ frac{cos20(-2(-sin20+frac{sqrt{3}}{2}+sqrt{3})}{2}$
$frac{sin40+sin40}{2}=sin40$