Question

Rewrite the expression as a single logarithm and simplify the result. ln lcosxl +lnltanxl

Answer 1

Recall your logarithms rules

$\bf ln|cos(x)|+ln|tan(x)|\\\\ -----------------------------\\\\ log_{{ a}}(xy)\implies log_{{ a}}(x)+log_{{ a}}(y)\qquad thus\\\\ -----------------------------\\\\ ln|cos(x)tan(x)|\implies ln\left| cos(x)\cdot \cfrac{sin(x)}{cos(x)} \right|\implies ln|sin(x)|$