(sinα +cosα)²-2sinα cosα =sin²α +2sinα cosα+cos²α -2sinα cosα =
=sin²α +cos²α=1
1 1 1
--------------------------------------- = --------------------- = ------------------------------- =
sin²α (sin²α +cos²α+ctg²α) sin²α (1+ctg²α) sin²α (1+cos²α/sin²α)
1 1
= ------------------ = ----------- =1
sin²α +cos²α 1
sin²(π+α )-cos²(π-α) (-sin²(α)) - (-cos²(α))
----------------------------------- = -------------------------------- =
tg²(π+α) - ctg²(π-α) tg²(α) - (-ctg²(α))
( (sin(α))² - (cos(α)) ² ) ((sin(α))² -(cos(α))²) *cos²(α)sin²(α)
= ------------------------------------------------ = ---------------------------------------------
( sin²(α)) / cos²(α)) - cos²(α) /sin²(α)) ( sin²(α))² - (cos²(α))²
((sin(α))² -(cos(α))²) *cos²(α)sin²(α)
-------------------------------------------------------- = cos²(α)sin²(α)
((sin(α))² -(cos(α))²)*((sin(α))² +(cos(α))²)