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
-
2/3
-
1/5
-
3/5
-
2/3
Solution
C.
3/5
A line makes angle θ with x-axis and z-axis and β with y-axis.
∴ l = cosθ, m = cosβ,n = cosθ
We know that, l2+ m2+ n2= 1
cos2θ + cos2β +cos2θ =1
2cos2θ = 1- cos2β
2cos2θ = sin2β
But sin2β = 3 sin2θ
therefore from equation (i) and (ii)
3sin2θ = 2cos2θ
3(1-cos2θ) = 2cos2θ
3-3cos2θ = 2cos2θ
3 = 5cos2θ
