Question

Найдите 10 cos a - 2 sin a + 10 / sin a - 5 cos a + 5, если tg a =5

Answer 1

(10cos a - 2sin a + 10)/(sin a - 5 cos a + 5) =
= -2 (-5cos a + sin a - 5)/(sin a - 5 cos a + 5) =
= - 2 (-5 + tg a -5 / cosa) / (tg a - 5 + 5/cos a) =
= - 2 (-5 + tg a -5 √(1 + tg²a)) / (tg a - 5 + 5 √(1 + tg²a)) =
= -2 (-5 + 5 - 5√(1 + 25)) / (5 - 5 + 5 √(1 + 25)) =
= 2