Sin²a=1:(1+ctg²a)=1:(1+2-2√2+1)=1/(4-2√2)
cos²a=1-sin²a=1-1/(4-2√2)²=1-1/(24-16√2)=(23-16√2)/(24-16√2)
cos2a=cos²a-sin²a=(23-16√2)/(24-16√2) -1/(4-2√2)=
=(23-16√2)/8(3-2√2)-1/(4-2√2)==(23-16√2)(3+2√2)/8(9-8) - (4+2√2)/(16-8)=
=(23-16√2)(3+2√2)/8 - (4+2√2)/8=(69+46√2-48√2-64-4-2√2)/8=(1-4√2)/8