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


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  • If the angle made by a line with coordinate axis are $\theta_1,\theta_2,\theta_3$, then $cos^2\theta_1+cos^2\theta_2+cos^2 \theta_3=1$
Given that the line makes angle $\theta$ with $x\:\:and\:\:z\:\:axis$ and $\beta$ with $y-axis$.
$\therefore\: co^2\theta+cos^2\theta+cos^2\beta=1$ and
also given that $sin^2\beta=3sin^2\theta$
From (i) and (ii) $1-2cos^2\theta=3cos^2\theta-2$
answered Dec 28, 2013 by rvidyagovindarajan_1
edited Sep 29, 2014 by sharmaaparna1
Okay, but there's a problem with this answer, when you put this value in cos2θ+cos2θ+cos2β=1 , you get  
    6/5+ cos2β =1, which is not possible, because it gives
    cos2β = -1/5

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