Answer
The formulas are equivalent.
Work Step by Step
Since the two LHS's are equal, we check if the RHS's are also equal.
The RHS of formula 1 =
$-\ln|\cos x|+C=(-1)\ln|\cos x|+C$
...Log Property: $n\ln M=\ln M^{n}...$
$=\displaystyle \ln(|\cos x|)^{-1}+C=\log|\frac{1}{\cos x} |+C$
... definition of sec: $\displaystyle \sec x=\frac{1}{\cos x}$ ...
$=\log|\sec x |+C$
$... $= The RHS of formula 2
Therefore, the formulas are equivalent.
