If 2 y \cos \\theta=x \sin \\theta and 2x \sec \\theta -y \cosec \\theta=3, then the value of (x^{2}+4 y^{2} ) is

SSC CGL Tier II 1 Dec 2016 Paper 1

Question : 91 of 100

Marks: +1, -0

2 y \cos \θ=x \sin \θ

and 2

x \sec \θ

-y \cosec \θ=3,

then the value of

(x^{2}+4 y^{2} )

Solution:

(4)

2 y \cos \θ=x \sin \θ..(i)

2 x \sec \θ-y \cosec \θ=3

⇒ 2 .{2 y \cos \θ}{\sin\θ} . \sec\θ-y \csc \θ =3

⇒ 4 y \cosec \θ-y \cosec \θ=3

⇒ 3 y \cosec \θ=3

⇒ y= {3}/{3 \cosec \θ}=\sin \θ

From equation (i),

2 \sin \θ. \cos \θ=x \sin \θ

⇒ x=2 \cos\θ

∴ x^{2}+4 y^{2}=4 \cos ^{2}\θ+4 \sin ^{2}\θ

=4 (\cos ^{2} \θ+\sin ^{2}\θ)=4

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