SSC CGL Model Paper 5

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Question : 51 of 100

Marks: +1, -0

QUANTITATIVE APTITUDE

If

\cosα + \cosβ = \sinα + \sinβ

then

\cos2α + \cos2β=?

$-2\sin (α+β)$
$2\cos (α-β)$
$2\sin (α+β)$
$- 2\cos (α+β)$

Solution:

ATQ

\cosα + \cosβ = \sinα + \sinβ

→ Squaring both sides,

\cos^2α + \cos^2β =2\cosα.\cosβ

=\sin^2α + \sin^2β+2\sinα . \sinβ

⇒

(\cos^2α-\sin^2α)+( \cos^2β -\sin^2β)

+2(\cosα.\cosβ-\sinα . \sinβ )=0

⇒

\cos2α + \cos2β + 2 \cos(α + β) = 0

⇒

\cos2α + \cos2β =- 2 \cos(α + β)

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