Establish each trig identity.
(1) In|tan(x)| = In|sin(x)| - In|cos(x)|
(2) In|sec(x) + tan(x)| + In|sec(x) - tan(x)| = 0
Also: Is In the symbol for natural log?
Why didn't you apply what you learned from logarithms in this forum here?
1.$\displaystyle \tan{x} = \frac{\sin{x}}{\cos{x}}$
$\displaystyle \ln{\tan{x}} = \ln{\frac{\sin{x}}{\cos{x}}} = \ln{\sin{x}} - \ln{\cos{x}}$
2. $\displaystyle \ln{(\sec{x} + \tan{x})} + \ln{(\sec{x} - \tan{x})}$
$\displaystyle \ln{[(\sec{x} + \tan{x})(\sec{x} - \tan{x})]}$
$\displaystyle \ln{(\sec^2{x} - \tan^2{x})}$
You should know that $\displaystyle 1 + \tan^2{x} = \sec^2{x}$
Thus:
$\displaystyle \ln{1} = 0$