Answer
Direction cosines are: $\frac{1}{\sqrt 3},\frac{1}{\sqrt 3},\frac{1}{\sqrt 3}$
Direction angles are: $55 ^\circ, 55^\circ, 55 ^\circ$
Work Step by Step
Given:$\lt c,c,c \gt$
Direction cosines are: $cos \alpha = \frac{c}{\sqrt {c^2+c^2+c^2}}=\frac {1}{\sqrt 3}, cos \beta =\frac{c}{\sqrt {c^2+c^2+c^2}}=\frac {1}{\sqrt 3}, cos \gamma=\frac{c}{\sqrt {c^2+c^2+c^2}}=\frac {1}{\sqrt 3}$
Thus, the direction angles are:
$ \alpha =cos^{-1} \frac {1}{\sqrt 3}=55 ^\circ, \beta = cos^{-1} \frac {1}{\sqrt 3}=55 ^\circ, \gamma = cos^{-1} \frac {1}{\sqrt 3}=55 ^\circ$