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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:

A
23
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B
15
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C
35
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D
25
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Solution

The correct option is A 35
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=12cos2θ=1cos2β
2cos2θ=sin2β ...(1)
But sin2β=3sin2θ ...(2)
From (1) and (2)
3sin2θ=2cos2θ3(1cos2θ)=2cos2θ33cos2θ=2cos2θ3=5cos2θ
cos2θ=35

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