recall your logarithms rules
[tex]\bf ln|cos(x)|+ln|tan(x)|\\\\
-----------------------------\\\\
log_{{ a}}(xy)\implies log_{{ a}}(x)+log_{{ a}}(y)\qquad thus\\\\
-----------------------------\\\\
ln|cos(x)tan(x)|\implies ln\left| cos(x)\cdot \cfrac{sin(x)}{cos(x)} \right|\implies
ln|sin(x)|[/tex]
