Ответы
3) ctg(α) = 1/tg(α)
sin(α) =tg(α) * cos(α)
cos(α) = sin(α) /tg(α)
4) cos(α) - ctg(α) cos(α) - (cos(α)/ sin(α))
---------------------------- = --------------------------------------- =
sin(α) - 1 sin(α) - 1
(cos(α) /sin(α) - cos(α) )/ sin(α) ( cos(α)* (sin(α) - 1 )/ sin(α)
= ---------------------------------------------- = ------------------------------------------ =
sin(α) - 1 sin(α) - 1
cos(α)
= ------------- = ctg (α)
sin (α)
cos²(α) -ctg²(α) cos²(α) - (cos²(α)/sin²(α))
----------------------------- * tg⁶(α) = ------------------------------------------ * tg⁶(α) =
sin²(α) - tg²(α) sin²(α) - (sin²(α)/cos²(α))
(cos²(α)*sin²(α) - cos²(α) ) /sin²(α))
= ------------------------------------------------------- * tg⁶(α) =
(sin²(α)*cos²(α) - (sin²(α) ) /cos²(α))
(cos²(α)*(sin²(α) - 1 ) /sin²(α))
= ------------------------------------------------------- * tg⁶(α) =
(sin²(α)*(cos²(α) - 1 ) /cos²(α))
(cos²(α)*cos²(α)) /sin²(α))
= ---------------------------------------------- * tg⁶(α) =
(sin²(α)*sin²(α)) /cos²(α))
(cos⁴(α)) /sin²(α)) cos⁴(α)*cos²(α)
= ------------------------------- * tg⁶(α) = ------------------------------- * tg⁶(α) =
(sin⁴(α)) /cos²(α)) sin⁴(α)*sin²(α)
cos⁶(α)
--------------- * tg⁶(α) = ctg⁶(α) * tg⁶(α) = 1
sin⁶(α)
sin⁴(α) -cos⁴(α) - sin²(α) +cos²(α) +1 =
= cos²(α) - cos⁴(α) - sin²(α)+ sin⁴(α) + 1 =
= cos²(α)*(1 - cos²(α) ) - sin²(α)*(1- sin²(α) + 1 =
= cos²(α)*(1 - cos²(α) ) - sin²(α)*(1- sin²(α) +1 =
= cos²(α)*sin²(α) - sin²(α)*cos²(α) +1 = 1