A line makes an angle theta with the X and Z | vedclass

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(A) Let the direction cosines of the line be $l, m, n$. Since the line makes an angle $	heta$ with $X$ and $Z$ axes,we have $l = \cos 	heta$ and $n

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$3/5$

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(A) Let the direction cosines of the line be $l, m, n$. Since the line makes an angle $	heta$ with $X$ and $Z$ axes,we have $l = \cos 	heta$ and $n = \cos 	heta$.Since the line makes an angle $\beta$ with the $Y$ axis,we have $m = \cos \beta$.We know that $l^2 + m^2 + n^2 = 1$.Substituting the values,we get $\cos^2 	heta + \cos^2 \beta + \cos^2 	heta = 1$.$2 \cos^2 	heta + \cos^2 \beta = 1$.Using the identity $\sin^2 \beta = 1 - \cos^2 \beta$,we have $\cos^2 \beta = 1 - \sin^2 \beta$.Substituting this into the equation: $2 \cos^2 	heta + (1 - \sin^2 \beta) = 1$.$2 \cos^2 	heta = \sin^2 \beta$.Given $\sin^2 \beta = 3 \sin^2 	heta$,we substitute this into the equation:$2 \cos^2 	heta = 3 \sin^2 	heta$.Using $\sin^2 	heta = 1 - \cos^2 	heta$:$2 \cos^2 	heta = 3(1 - \cos^2 	heta)$.$2 \cos^2 	heta = 3 - 3 \cos^2 	heta$.$5 \cos^2 	heta = 3$.$\cos^2 	heta = 3/5$.

$A$ line makes an angle $\theta$ with the $X$ and $Z$ axes and an angle $\beta$ with the $Y$ axis. If $\sin^2 \beta = 3 \sin^2 \theta$,then $\cos^2 \theta = \dots$

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