[JEE Main 2004] a line makes the same angle theta with the x and z axes and
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
(a) $\frac25$
(b) $\frac15$
(c) $\frac35$
(d) $\frac23$
1 Answer
VAVidaara Admin
✓ Vidaara Team
✓ Accepted
· 2d ago
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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.
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