A line makes the same angle θ, with each of the x and z axis.
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:
(a) 3/5
(b) 1/5
(c) 2/3
(d) 2/5.
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(a) : If a line makes the angle α, β, γ with x, y, z axis respectively then
l2 + m2 + n2 = 1
=> 2l2 + m2 = 1 or 2n2 + m2 = 1
=> 2cos2θ = 1 – cos2β (α = γ = θ)
2cos2θ = sin2 β
=> 2cos2θ = 3sin2θ (given sin2β = 3sin2θ)
=> 5cos2θ = 3
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