Ответ(ы) на вопрос:
Гостьsin (2α) -tg(α) =2sin(α)cos(α) - (sin(α)/cos(α) ) приведем о общ. знаменателю
2sin(α)cos(α)*cos(α) - (sin(α) 2sin(α)cos(α)²- (sin(α)
----------------------------------------- = ---------------------------------
соs(α) cos(α)
(sin(α)* (2cos(α)²- 1)
----------------------------------------- = tg(α)*cos(2α)
cos(α)
----------------------------------------------------------------------------------------------------
cos(α) sin(α)
ctg(α)- tg(α) = --------- - ------------ приведем о общ. знаменателю
sin(α) cos(α)
cos²(α) - sin²(α) cos(2α)
-------------------------- = --------------- = 2ctg(2α)
sin(α) * cos(α) sin(2α) /2
к сведению : sin(2α)) =2sin(α)cos(α)⇒ sin(α)cos(α)=sin(2α)/2
------------------------------------------------------------------------------------------------
sin(2α) -ctg(α)= 2sin(α)cos(α) - cos(α) / sin(α)
2sin(α)cos(α)*sin(α) - cos(α) 2sin(α)²cos(α)- cos(α)
----------------------------------------- = ----------------------------------------
sin(α) sin(α)
cos(α)*(2sin²(α)-1)
---------------------------- = ctg(α)*(2sin²(α)-1)= -ctg(α)*cos(2α)
sin(α)
заметим ,что cos(2α)=1-2sin²(α) = -(2sin²(α)-1)
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