Question

синус 30 градусов плюс альфа минус косинус 60 градусов плюс альфа
sin(30 + α) - cos(60 + α)
sin(30 + α) + cos(60 + α)

Answer 1

$frac{sin(30+ alpha)-cos(60+ alpha )}{sin(30+ alpha) +cos(60+ alpha)} = frac{sin30cos alpha +cos30sin alpha-(cos60cos alpha-sin60sin alpha )}{sin30cos alpha +cos30sin alpha+cos60cos alpha-sin60sin alpha } =$
$=frac{ frac{1}{2} cos alpha+ frac{ sqrt{3}}{2} sin alpha- frac{1}{2} cos alpha+frac{ sqrt{3}}{2} sin alpha}{frac{1}{2} cos alpha+frac{ sqrt{3}}{2} sin alpha +frac{1}{2} cos alpha-frac{ sqrt{3}}{2} sin alpha}=$
$=frac{ sqrt{3}sin alpha }{cos alpha } = sqrt{3} tg alpha$