Question

If $-\pi \le x\le \pi$, $-\pi \le y\le \pi$ and $\cos x+\cos y=2$ then the value $\cos (x-y)$

• A. -1
• B. 0
• C. 1
• D. none of these

Answer 1

The correct option is C 1

$\cos x+\cos y=2$
but we know that maximum value of $\cos x$ is 1
hence only solution is $\cos x=1$ and $\cos y=1$
so in $-\pi \le x\le \pi ,-\pi \le y\le \pi$
solution is $x=0,y=0$
therefore,
$\cos (x-y)=1$
Hence, option 'C' is correct.