Show that the direction cosines of a vector equally inclined to the axes OX, OY and OZ are

Firstly,

Let’s assume a vector to be equally inclined to axes OX, OY, and OZ at angle 

   

.

Then, the direction cosines of the vector are

   

,

   

and

   

.

Now, we know that

Therefore, the direction cosines of the vector which are equally inclined to the axes are

   

,

   

,

   

.

Hence proved.