If Tan α = 12, then (sin α + cos α) 2cos2 α=______ ．

If Tan α = 12, then (sin α + cos α) 2cos2 α=______ ．

(sin α + cos α) 2 = sin 2 α + 2 sin α cos α + Cos2 α, Cos2 α = cos 2 α, Cos2 α = cos 2 α - Sin 2 α (sin α + cos α) 2cos2 α = Sin & nbsp; 2 α + 2 sin α cos α + cos α (2 α + cos α) 2cos2 α = Sin & nbsp; 2 α + 2 sin α cos α + cos & nbsp; 2 α & nbsp; 2 α & nbsp; 2 α & nbsp; 2 α + 2 sin α + 2 sin α cos α (Cos2 α) 1 cos 2 (Cos2 α) 1 (Cos2 α) 1 Cos2 α (COS & nbsp; Co & nbsp; Co & nbsp; 2 α & nbsp; Co & nbsp; 2 α & nbsp; 2 α & nbsp; this is the case & nbsp; 2 α & nbsp; 2 α & nbsp; and the two & nbsp; 2 α & nbsp; and the & nbsp; 2 α & nbsp; 2; the; the; the; 2 α & nbsp; 2 α & nbsp; 2 α & nbsp; = 3, so the answer is: 3