Use the trigonometric identity:
[tex]\cos { \left( A+B \right) = } \cos { \left( A \right) } \cos { \left( B \right) } -\sin { \left( A \right) \sin { \left( B \right) } } [/tex]
Now, if A=2u and B=2u:
[tex]\cos { \left( 2u+2u \right) } \\ \\ =\cos { \left( 4u \right) } \\ \\ =\cos { \left( 2u \right) } \cos { \left( 2u \right) } -\sin { \left( 2u \right) \sin { \left( 2u \right) } } \\ \\ =\cos ^{ 2 }{ \left( 2u \right) -\sin ^{ 2 }{ \left( 2u \right) } } [/tex]
