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Q.

$Let a line make an angle θ with X and Z -axes and β with Y -axis. If \sin (β) = \sqrt{3} \sin θ,$ $then \cos^{2} θ =$

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a

$\frac{3}{5}$

b

$\frac{5}{3}$

c

$\frac{1}{5}$

d

$\frac{2}{5}$

answer is A.

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Detailed Solution

$W e h a v e \cos^{2} θ + \cos^{2} β + \cos^{2} θ = 1$

$\Rightarrow 2 \cos^{2} θ = \sin^{2} β$

$\Rightarrow 2 \cos^{2} θ = 3 \sin^{2} θ$

$\Rightarrow 2 \cos^{2} θ = 3 - 3 \cos^{2} θ$

$\Rightarrow 5 \cos^{2} θ = 3$

$\Rightarrow \cos^{2} θ = \frac{3}{5}$

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