# If sec a + cos a = 5/2, then find sec a - cos a ?

${\left(\sec a - \cos a\right)}^{2} = {\left(\sec a + \cos a\right)}^{2} - 4 \sec a \times \cos a$
$\implies {\left(\sec a - \cos a\right)}^{2} = {\left(\frac{5}{2}\right)}^{2} - 4 \times 1$
$\implies \sec a - \cos a = \sqrt{\frac{25}{4} - 4} = \sqrt{\frac{9}{4}} = \frac{3}{2}$