Since,

the normal to the plane is equally inclined to the axes.

so,

\[cos\text{ }\alpha \text{ }=\text{ }cos\text{ }\beta \text{ }=\text{ }cos\text{ }\gamma \]

or,

\[So,\text{ }co{{s}^{2}}~\alpha \text{ }+\text{ }co{{s}^{2}}~\alpha \text{ }+\text{ }co{{s}^{2}}~\alpha \text{ }=\text{ }1\]

\[3\text{ }co{{s}^{2}}~\alpha \text{ }=\text{ }1\Rightarrow cos\text{ }\alpha \text{ }=\text{ }\pm \text{ }1/\surd 3\]

Or ,

\[~cos\text{ }\alpha \text{ }=\text{ }cos\text{ }\beta \text{ }=\text{ }cos\text{ }\gamma \text{ }=\text{ }\pm \text{ }1/\surd 3\]