1)1-2cosα+cos2α=sin²α+cos²α-2cosα+cos²α-sin²α=2cos²α-2cosα=
2cosα(cosα-1)=2cosα(cos²α/2-sin²α/2-sin² α/2-cos² α/2)= -4cosα sin² α/2. ч.т.д.
2)1-sinα-cosα=(1-cosα)-sinα=2sin² α/2-2sin α/2·cos α/2=2sin α/2(sin α/2-
-cos α/2)=2sin α/2·(cos(π/2-α/2)-cos α/2)=2sin α/2·( -2sin(π/4-α/2)·sin π/4)=
=2√2sin α/2·sin(α/2-π/4). ч.т.д.
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Answers & Comments
1)1-2cosα+cos2α=sin²α+cos²α-2cosα+cos²α-sin²α=2cos²α-2cosα=
2cosα(cosα-1)=2cosα(cos²α/2-sin²α/2-sin² α/2-cos² α/2)= -4cosα sin² α/2. ч.т.д.
2)1-sinα-cosα=(1-cosα)-sinα=2sin² α/2-2sin α/2·cos α/2=2sin α/2(sin α/2-
-cos α/2)=2sin α/2·(cos(π/2-α/2)-cos α/2)=2sin α/2·( -2sin(π/4-α/2)·sin π/4)=
=2√2sin α/2·sin(α/2-π/4). ч.т.д.