Номер 250 помогите плиз

Решите задачу:

$\frac{1}{sin170} - \frac{\sqrt3}{sin100} = \frac{1}{sin(180-10)} -\frac{\sqrt3}{sin(90+10)} =\\\\= \frac{1}{sin10} -\frac{\sqrt3}{cos10} = \frac{cos10-\sqrt3sin10}{sin10\cdot cos10} = \frac{2(\frac{1}{2}cos10-\frac{\sqrt3}{2}sin10)}{\frac{1}{2}sin20} =\\\\= \frac{2(sin30\cdot cos10-cos30\cdot sin10)}{\frac{1}{2}sin20} = \frac{4\cdot sin(30-10)}{sin20} = \frac{4\cdot sin20}{sin20} =4$