Question

A line makes the same angle θ with each of the x- and z-axis. If the angle β, which it makes with y-axis, is such that sin²β  = 3sin²θ, then cos²θ equals. 

Answer 1

We know that

cos²α + cos²β + cos²γ = 1

Since line makes angle θ with x- and z-axis and angle β with y-axis.