((sin(x)-cos(x))^2-1+sin(4x))/(cos(2x)+cos(4x)) знаю - вопрос №7586898214243 от ivchencov767 21.07.2020 03:01

Question

Математика: ((sin(x)-cos(x))^2-1+sin(4x))/(cos(2x)+cos(4x)) знаю ответ, tg3x, решаю, прийти к нему не могу.

ivchencov767 · Answer

(sin X - cos X)² - 1 + sin 4Х
=
cos 2Х + cos 4X

sin² X - 2sin X * cos X + cos² X - 1 + sin 4X
= =
   cos 2X + cos² 2X - sin² 2X

-2sin X * cos X + sin 4X
= =
cos 2X + cos² 2X - (1 - cos² 2X)

-sin 2X + 2 * sin 2x * cos 2X
= =
cos 2X + cos² 2X - 1 + cos² 2X

sin 2X * (2cos 2X - 1)
= =
cos 2X * (1 + cos 2X) + (cos² 2X - 1)

sin 2X * (2cos 2X - 1)
= =
cos 2X * (cos 2X + 1) + (cos 2X + 1)*(cos 2X - 1)

sin 2X * (2cos 2X - 1)
= =
(cos 2X + 1) * (cos 2X + cos 2X - 1)

sin 2X * (2cos 2X - 1)
= =
(cos 2X +1) * (2cos 2X - 1)

sin 2X   2 * sin X * cos X
= = =
cos 2X + 1 cos² X - sin² X + sin² X + cos² X

2 * sin X * cos X sin X * cos X sin X
= = = = tg X
  2cos² X cos X * cos X    cos X