[tex]sec (a - b) = \frac{sec(a)sec(b)}{1 + tan(a)tan(b)} \\ =\frac{ \frac{1}{cos (a)} ( \frac{1}{cos (b)})}{1 + ( \frac{sin (a)}{cos(a)}) ( \frac{sin(b)}{cos(b)}) } \\ = \frac{ \frac{1}{(cos(a)cos(b)} }{ \frac{cos(a)cos(b)+sin(a)sin(b)}{cos(a)cos(b)} } \\ = \frac{1}{cos(a)cos(b)+sin(a)sin(b)} \\ = \frac{1}{cos(a - b)} \\ = sec (a - b)[/tex]
