A line makes the same angle θ, with each of the x and z axes. If the angle β, which it makes with y-axis is such that sin 2 β=3 sin 2 θ, then find value of 5 cos 2 θ.

Question

A line makes the same angle θ, with each of the x and z axes. If the angle β, which it makes with y-axis is such that sin 2 β=3 sin 2 θ, then find value of 5 cos 2 θ. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

cos 2 θ+ cos 2 β+ cos 2 θ=1 ⇒ 2 cos 2 θ= sin 2 β but sin 2 β=3 sin 2 θ So, 3 sin 2 θ=2 cos 2 θ ⇒ 5 cos 2 θ=3

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

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

Q. A line makes the same angle θ, with each of the x and z axes. If the angle β, which it makes with y-axis is such that sin2β=3sin2θ, then find value of 5cos2θ.

cos2θ+cos2β+cos2θ=1 ⇒2cos2θ=sin2β but sin2β=3sin2θ So, 3sin2θ=2cos2θ ⇒5cos2θ=3

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

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