SSC CGL Tier II 12 Jan 2017 Paper 1

Question : 88 of 100

Marks: +1, -0

If cosx . cosy + sinx . siny = –1 then cosx + cosy is

Solution:

(3) cosx . cosy + sinx. siny = –1
⇒ cosx . cosy + 1 = – sinx . siny
On squaring both sides,

(\cos x . \cos y+1)^{2}=\sin ^{2} x \sin ^{2} y

⇒ \cos ^{2} x . \cos ^{2} y+2 \cos x . \cos y +1

= (1-\cos ^{2} x ) (1-\cos ^{2} y )

⇒\cos ^{2} x . \cos ^{2} y+2 \cos x . \cos y +1

=1-\cos ^{2} x-\cos ^{2} y+\cos ^{2} x \.\cos ^{2} y

⇒ \cos ^{2} x+\cos ^{2} y+2 \cos x. \cos y =0

⇒(\cos x+\cos y)^{2}=0

⇒ \cos x+\cos y=0

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