Question

If $sinx+siny=0=cosx+cosy$, then $cos2x+cos2y$ is equal to

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

Answer 1

Answer: (B)

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