Question

Sketch the graph for $y=1+3(\log \left|\sin x\right|+\log \left|\csc x\right|)$

Answer 1

$y=1+3(\log \left|\sin x\right|+\log \left|\csc x\right|)$
is defined whenever $\left|\sin x\right|\ne 0$ and $\left|\csc x\right|\ne 0$
i.e., $y=1+3\left(\log 1\right)$ whenever $x\notin n\pi ,x\in Z$
$\Rightarrow y=1$ as $\log 1=0$
$\therefore$ Domain $\in R-\{n\pi :n\in Z\}$
and Range$\in \left\{1\right\}$
$\therefore$ it could be plotted as shown below.
Thus, the curve for $y=1+3(\log \left|\sin x\right|+\log \left|\csc x\right|)$ is shown below.