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sin²α+cos²α+2 (sinα-cosα)+2-3=
1+2(sinα-cosα)-1= 2(sinα-cosα)
b)sin(do potęgi 4)-cos(do potęgi 4)α=
sin⁴α-cos⁴α= (sin²α-cos²α)(sin²α+cos²α)= sin²α-cos²α
sin²α+cos²α = 1
I:
cos²α - sin²α = cos2α
sin²α - cos²α = -cos2α
a)
(sin α +1)²+(cos α-1)²-3
sin²α+2sinα+1+cos²α-2cosα+1-3 = 1+1+1+2sinα-2cosα-3 =
= 2sinα-2cosα
b)
sin[4]α-cos[4]α = (sin²α + cos²α)(sin²α - cos²α) = sin²α - cos²α =
= -cos2α