What is the sum of the squares of direction cosines of x -axis?

Angle made by $x$-axis with $x$-axis, $y$-axis and $z$-axis are $0^{{}^{\circ}}, 90^{{}^{\circ}} \ \text{ and } 90^{{}^{\circ}}$ respectively, therefore its direction cosines are $\cos$\left(0^{{}^{\circ}}\right), \cos \left(90^{{}^{\circ}}\right), \cos \left(90^{{}^{\circ}}\right)$i.e.,$1,0,0$. Sum of the square of direction cosines$=(1)^2+(0)^2+(0)^2=1