Question

1/sin170° - $sqrt{3}$ /sin 100° чему равно значение выражения

Answer 1

$frac{1}{sin170^circ }-frac{sqrt3}{sin100^circ} = frac{1}{sin(180-10)}-frac{sqrt3}{sin(90+10)} = frac{1}{sin10} -frac{sqrt3}{cos10} =\\= frac{cos10-sqrt3cdot sin10}{sin10cdot cos10} =frac{cos10-tg60cdot sin10}{frac{1}{2}sin20} = frac{cos10-frac{sin60}{cos60}cdot cos10}{frac{1}{2}sin20} =\\= frac{2cdot (cos60cdot cos10-sin60cdot sin10)}{cos60cdot sin20} = frac{2cdot cos(60+10)}{frac{1}{2}cdot sin(90-70)}= frac{4cdot cos70}{cos70} =4$