#sec (x) = 1/cos (x)#
and,
#cot (x) = cos(x)/sin(x)#
expanding the given function;
#1/cos^2(x) * cos(x)/sin(x) - cos(x)/sin(x)#
#=> 1/(cos(x)*sin(x)) - cos(x)/sin(x)#
Multiplying the numerator and denominator of #cos(x)/sin(x)# by #cos(x)# we get the same denominators for both terms.
#=> 1/(cos(x)*sin(x)) - cos^2(x)/(cos(x) *sin(x))#
Then we can simplify further by taking common denominator;
#=> (1- cos^2(x))/(cos(x)*sin(x))#
we know, that #1- cos^2(x) = sin^2(x)#
Therefore, we have
#sin^2(x) / (cos(x)*sin(x))#
#=>sin^(cancel(2))(x)/ (cos(x)*cancel(sin(x)))#
#=> sin(x) / cos(x)#
#=> tan(x)#