Question

If $\cos^{-1} x +\cos^{-1} y +\cos^{-1}z = 3\pi$, then $xy + yz + zx$ is

• A. 1
• B. 0
• C. -3
• D. 3

Answer 1

Answer: (D)

3

Answer 2

$\cos^{-1} x +\cos^{-1} y +\cos^{-1}z = 3\pi$
We know that $0\le\cos ^{-1}x \le\pi$
$\Rightarrow \cos ^{-1} x =\cos ^{-1}y =\cos ^{-1}z =\pi$
$\Rightarrow x = y=z= -1$
Now, $xy+yz+zx$
$= \left(-1\right)\left(-1\right)+\left(-1\right)\left(-1\right)+\left(-1\right)\left(-1\right)=3$