SSC CGL Tier II 25 Oct 2015 Paper 1

Question : 31 of 100

Marks: +1, -0

If x = a sin θ – b cos θ, y = a cos θ + b sin θ, then which of the following is true?

Solution:

(4) x = a sinθ – b cosθ --- (i)
y = a cosθ + b sinθ --- (ii)
On squaring and adding both the equations,

x^{2}+y^{2}=(a \sin \θ-b \cos \θ)^{2}+

(a \cos \θ+b \sin \θ)^{2}

=a^{2} \sin ^{2} \θ+b^{2} \cos ^{2} \θ-2 a b \sin \θ

. \cos \θ+a^{2} \cos ^{2} \θ+b^{2} \sin ^{2} \θ+

a b \sin \θ . \cos \θ

=a^{2} (\sin ^{2} \θ+\cos ^{2} \θ )+b^{2} (\cos ^{2} \θ+ .

\sin ^{2} \θ )

=a^{2}+b^{2}

[∵ \sin ^{2} \θ+\cos ^{2} \θ=1 ]

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