Giải phương trình: 2008cos^2009 x +2009sin^2008 x =4017

\(\eqalign{ & 2008{\cos ^{2009}}x + 2009{\sin ^{2008}}x = 4017 \cr & \left\{ \matrix{ {\cos ^{2009}}x \le 1 \Rightarrow 2008{\cos ^{2009}}x \le 2008 \hfill \cr {\sin ^{2008}}x \le 1 \Rightarrow 2009{\sin ^{2008}}x \le 2009 \hfill \cr} \right. \cr & \Rightarrow VT \le 4017 \cr & Dau\,\,'' = ''\,\,xay\,\,ra \cr & \Leftrightarrow \left\{ \matrix{ {\cos ^{2019}}x = 1 \hfill \cr {\sin ^{2018}}x = 1 \hfill \cr} \right. \Leftrightarrow \left\{ \matrix{ \cos x = 1 \hfill \cr \left[ \matrix{ \sin x = 1 \hfill \cr \sin x = - 1 \hfill \cr} \right. \hfill \cr} \right.\,\,\left( {Vo\,\,nghiem} \right) \cr} \) Vậy phương trình đã cho vô nghiệm.