Question

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

Answer 1

Here, $y=1+3(\log \sin x+\log \csc x)$
is defined whenever $\sin x>0$ and $\csc x>0$
$\Rightarrow y=1+3\log 1;$ for $x\in (2n\pi ,(2n+1)\pi )$
or $y=1$ whenever $x\in (2n\pi ,(2n+1)\pi )$
$\therefore y=1+3(\log \sin x+\log \csc x)=\{1;2n\pi <x<(2n+1)\pi \}$ is as shown below:
Thus the curve for $y=1+3(\log \sin x+\log \csc x)$