Sin(α -π/4) / sin(α +π/4) * ctq(α - 5π/4) - cos(π/2 +α)*sin(α - π) =
sin(-(π/4 - α)) / sin(π/2 -(π/4 -α)) * ctq( -(π+π/4 - α ) ) -(-sinα)*sin( -(π -α) ) =
-sin(π/4 -α) / cos(π/4 -α) *(- ctq(π+π/4 - α ) ) - sin α*sin (π -α) =
tq(π/4 - α)*ctq(π+(π/4 - α ) ) - sin α*sin α =tq(π/4 - α)*ctq(π/4 - α) - sin² α =
1 -sin² α =cos²α.