Question

Докажите тождество

cos(2a+п)=cos^2(a-п/2)+cos(a+п)sin(a+п/2)

Answer 1

cos(2α+π)=cos²(α-π/2)+cos(α+π)·sin(α+π/2);⇒
cos(2α+π)=-cos2α;
cos²(α-π/2)+cos(α+π)·sin(α+π/2)=cos²(-(π/2-α))-cosα·cosα=
=sin²α-cos²α=-cos2α;⇒
-cos2α=-cos2α;