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Q.

A line makes the same angle $θ$ , with each of the x and z-axes. If the angle $β$ , which it makes with y-axis, is such that sin² $β$ = 3sin² $θ$ then cos² $θ$ equals.

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a

3/2

b

1/5

c

3/5

d

2/5

answer is A.

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Detailed Solution

l²+m²+n²=1
$\begin{array}{l} 2 \cos^{2} θ + \cos^{2} β = 1 \\ 2 \cos^{2} θ = \sin^{2} β \\ Given \sin^{2} β = 3 \sin^{2} θ \\ \sin^{2} β = 3 \sin^{2} θ \\ \Rightarrow 2 \cos^{2} θ = 3 - 3 \cos^{2} θ \\ \Rightarrow \cos^{2} θ = 3 / 5 \end{array}$

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