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

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;