Question

If sec A + tan A = p, find sec A - tan A.

Answer 1

Given that,
$\sec(x) + \tan(x) = p$
Using Identity,
${ \sec }^{2} x - { \tan }^{2} x = 1$
$[ \sec(x) - \tan(x) ][ \sec(x) + \tan(x) ] = 1$
$[\sec(x) - \tan(x) ] \times p = 1$
$\boxed{\sec(x)-\tan(x)=\frac{1}{p}}$