Thank you for reporting, we will resolve it shortly
Q.
If a line makes angles $\frac{\pi}{4}$ and $\frac{\pi}{3}$ with $Y$ -axis and $Z$ -axis respectively, then the obtuse angle made by that line with $X$ - axis is
Let line makes angle $\alpha$ with $X$ -axis then, direction cosine of the line are
$l=\cos \alpha, m=\cos \frac{\pi}{4}, n=\cos \frac{\pi}{3} $
But $l^{2}+m^{2}+n^{2}=1$
$l^{2}+\left(\frac{1}{\sqrt{2}}\right)^{2} +\left(\frac{1}{2}\right)^{2}=1 $
$l^{2}+\frac{1}{2}+\frac{1}{4} =1 $
$l^{2}=\frac{1}{4}$
$ \Rightarrow l =\pm \frac{1}{2}$
$\Rightarrow \cos \alpha=-\frac{1}{2}(\alpha$ is obtuse angle $)$
$\Rightarrow \alpha=\pi-\pi / 3=2 \pi / 3$