(tga*tg2a)/(tg2a-tga) спростити

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)