Concept : If a line makes the angle α,β,γ with x,y,z axis respectively then cos2α+cos2β+cos2γ=1 In this question given that the line makes angle θ with x and z-axis and β with y-axis. ∴cos2θ+cos2β+cos2θ=1 ⇒2cos2θ=1−cos2β ⇒2cos2θ=sin2β But given that sin2β=3sin2θ ∴2cos2θ=3sin2θ ⇒2cos2θ=3(1−cos2θ) ⇒2cos2θ=3−3cos2θ ⇒5cos2θ=3 ⇒cos2θ=