A line makes the same angle $ heta$, with each of the $x$ and $z$ axis. If the angle $\beta$, which it makes with $y$-axis, is such that $\sin ^2 \beta=3 \sin ^2 heta$, then $\cos ^2 heta$ equals

Question

A line makes the same angle $	heta$, with each of the $x$ and $z$ axis. If the angle $\beta$, which it makes with $y$-axis, is such that $\sin ^2 \beta=3 \sin ^2 	heta$, then $\cos ^2 	heta$ equals

Aicharya · Accepted Answer

$I=\cos 	heta, m=\cos 	heta, n=\cos \beta$ $\cos ^2 	heta+\cos ^2 	heta+\cos ^2 \beta=1 \Rightarrow 2 \cos ^2 	heta=\sin ^2 \beta=3 \sin ^2 	heta \quad$ (given) $\cos ^2 	heta=3 / 5$

A line makes the same angle $\theta$, with each of the $x$ and $z$ axis. If the angle $\beta$, which it…

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