(sin112.5°)^4-(cos112.5°)^4 =[(sin112.5°)^2+(cos112.5°)^2]*[(sin112.5°)^2-(cos112.5°)^2] =(sin112.5°)^2-(cos112.5°)^2 = -[(cos112.5°)^2-(sin112.5°)^2] = -cos225° =cos45° =√2/2 .
