The answer is option A
Given below is the steps to solve this problem.
At first consider the fact that there are 3 unknowns and only 2 equations are given.
But we know the general property of direction cosines.
They are governed by the equation;
Now we have 3 equations and 3 unknowns.
Now write l in terms of m and n, this will reduce the number of variables to two.
Substitute this in second equation.
Now you will get 2 equation and 2 unknowns.
Substitute this in third equation to get the final third degree equation.
Solving this will give the above mentioned result.