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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class11  >>  3-D Geometry
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A line makes angle $\theta$ with both $x\:axis$ and $z\:axis$. If it makes angle $\alpha$ with $y\:axis$ and $\sin^2\alpha=2 \sin^2\theta$ then $\cot^2\theta=?$


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Since the line makes angle $\theta,\alpha\:and\:\theta$ with the coordinate axes,
Given: $ sin^2\alpha=2sin^2\theta$
$\Rightarrow\:cos^2 \alpha=2cos^2\theta-1$.....(ii)
Solving (i) and (ii), $cos^2\theta=\large\frac{1}{2}$
answered Jan 6, 2014 by rvidyagovindarajan_1

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