SSC CGL 7 Sep 2016 Paper

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Question : 70 of 100

Marks: +1, -0

If x = a cos θ cos θ , y = a cos θ sin θ and z = a sin θ , then the value of (

x^2 + y^2 + z^2

) is

$2a^2$
$4a^2$
$9a^2$
$a^2$

Solution:

x = a cos θ . cos ϕ
y = a cos θ . sin ϕ
z = a sin θ
∴

x^2 + y^2 + z^2

=

a^2

cos^2

ϕ .

cos^2

θ +

a^2

cos^2

θ .

sin^2

ϕ +

a^2

sin^2

θ
=

a^2

cos^2

θ (

cos^2

ϕ +

sin^2

ϕ ) +

a^2

sin^2

θ
=

a^2

cos^2

θ +

a^2

sin^2

θ
=

a^2

(

cos^2

θ +

sin^2

θ ) =

a^2

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