Simplify: cos x cos x

Question

----- + -----
sec x-1 sec x+1

Answer 1

is that
cosx/(secx - 1) + cosx/(secx + 1) ???

of so, then using a common denominator , ...
(cosx(secx + 1) + cosx(secx - 1)) / (sec^2 x - 1)
= cosx(2secx)/tan^2x
= cosx(2/cosx) ( cos^2x/sin^2x
= 2cot^2 x