(tga*tg2a)/(tg2a-tga) спростити. Created by umnichka1o1. algebra-ru

(tga*tg2a)/(tg2a-tga)=(tga*2tga/(1-tg^2a))/(2tga/(1-tg^2a)-tga)==(2tg^2a/(1-tg^2a))/((tga(1-tg^2a)/(1-tg^2a)=2tg^2a/(1-tg^2a)*1/tga==2tga/(1-tg^2a)=tg2a

(tg2a-tga) спростити...

MizoriesKun Числитель: (tga*tg2a)

sin(α) sin(2α) sin(α)* 2sin(α) cos(α) 2 sin²(α)cos(α)
---------- * ----------- = -------------------------------- = ----------------------------
cos(α) cos(2α) cos(α) * cos(2α) cos(α) * cos(2α)

знаменатель : (tg2a-tga)

sin(2α) sin(α) sin(2α)* cos(α) - sin(α)* cos(2α)
------------ - --------------- = ---------------------------------------------- =
cos(2α) cos(α) cos(2α) * cos(α)

2 sin(α) cos(α) * cos(α) - sin(α)*(2cos²(α) -1 )
= ----------------------------------------------------------------------- =
cos(2α) * cos(α)

2 sin(α) cos²(α) - 2cos²(α) sin(α) +sin(α)       sin(α)
= --------------------------------------------------------------- = -------------------------------
cos(2α) * cos(α) cos(2α) * cos(α)

решаем

2 sin²(α)cos(α) sin(α) 2 sin²(α)cos(α) cos(2α) *cos(α)
-------------------------- : ---------------------- = ----------------------- *-------------------------
  cos(2α) *cos(α) cos(2α) *cos(α) cos(2α) *cos(α) sin(α)

2 sin²(α)cos(α)
= -------------------------- = 2 sin(α)cos(α) =sin(2α)
sin(α)

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