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