Question

Чему равно выражение (1-tg2x tgx) (1+tg2x tgx), и почему

Answer 1

(1-tg2x tgx) (1+tg2x tgx) =?

числитель = 1 - tg2x tgx = 1 - Sin2x/Cox2x * Sinx/Cosx =

= (Cos2xCosx -Sin2xSinx)/(Cos2xCosx) = Cos(2x+x) /(Cos2xCosx) =

=Cos3x/(Cos2xCosx)

знаменатель = 1 + tg2x tgx = 1 + Sin2x/Cox2x * Sinx/Cosx =

= (Cos2xCosx + Sin2xSinx)/(Cos2xCosx) = Cos(2x-x) /(Cos2xCosx) =

=Cosx/(Cos2xCosx) = 1/Cos2x

Теперь сама дробь =

= Cos3x/(Cos2xCosx) : 1/Cos2x = Cos3x/Cosx