[JEE Main 2004] A line makes the same angle $\theta$ with the $x$- and $z$-axes, and angle $\beta$ with the $y$-axis where $\sin^2\beta=3\sin^2\theta$. Then $\cos^2\theta$ equals

Correct answer: (c) $\frac35$

Direction cosines: $2\cos^2\theta+\cos^2\beta=1\Rightarrow\sin^2\beta=2\cos^2\theta$. With $\sin^2\beta=3\sin^2\theta=3(1-\cos^2\theta)$: $2\cos^2\theta=3-3\cos^2\theta\Rightarrow\cos^2\theta=\frac35$.

JEE Main 2004 · Trigonometry — verified solution by the Vidaara Team.