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

Correct answer: (C) 3/5. I=cos θ, m=cos θ, n=cos β cos^2 θ+cos^2 θ+cos^2 β=1 ⇒ 2 cos^2 θ=sin^2 β=3 sin^2 θ (given) cos^2 θ=3 / 5

Q130 / 225 · JEE Main 2004 · Mathematics

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

A
$\frac{2}{3}$
B
$\frac{1}{5}$
Correct answer
C
$\frac{3}{5}$
D
$\frac{2}{5}$

Solution

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

Hence, the correct answer is option: 'C'.

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