Question

Тригонометрия. Вычислите:
$frac{1+cos50-cos25}{sin50-sin25}-tg65$

Answer 1

числитель =

=1 + Cos50° -Cos25° = 1 + 2Cos²25° -1 -Cos25° = 2Cos²25° -Cos25° =

=Cos25°(2Cos25° -1)

знаменатель = 2Sin25°Cos25° -Sin25° = Sin25°(2Cos25° -1)

Сама дробь = Ctg25°

Наш пример:

Ctg25° - tg65° = tg65° - tg65° = 0         (Сtg65° = Ctg(90° -25°) = tg25° )