Question

A line makes the same angle $\theta$, with each of the $x$ and $z$ axes. If the angle $\beta$, which it makes with $y$-axis is such that $\sin ^{2} \beta=3 \sin ^{2} \theta$, then find value of $5 \cos ^{2} \theta$.

Answer 1

$\cos ^{2} \theta+\cos ^{2} \beta+\cos ^{2} \theta=1$
$\Rightarrow 2 \cos ^{2} \theta=\sin ^{2} \beta$
but $\sin ^{2} \beta=3 \sin ^{2} \theta$
So, $3 \sin ^{2} \theta=2 \cos ^{2} \theta$
$\Rightarrow 5 \cos ^{2} \theta=3$