Question

If $sin\, x + sin\, y = 0 = cos\, x + cos\, y$, then $cos \,2x + cos\, 2y$ is equal to

• A. $ -2\,sin(x + y) $
• B. $ -2\,cos(x + y)$
• C. $2\,sin(x + y)$
• D. $ 2\,cos(x + y)$

Answer 1

Answer: (B)

Consider,
$(\cos x+\cos y)^{2}-(\sin x+\sin y)^{2}=0$
$\Rightarrow \left(\cos ^{2} x+\cos ^{2} y+2 \cos x \cos y\right)$
$-\left(\sin ^{2} x+\sin ^{2} y+2 \sin x \sin y\right)=0$
$\Rightarrow \,\cos 2 x+\cos 2 y=-2(\cos x \cos y-\sin x \sin y)$
$\Rightarrow \, \cos 2 x+\cos 2 y=-2 \cos (x+y)$