Search any question & find its solution
Question:
Answered & Verified by Expert
If $\cos ^{-1} x+\cos ^{-1} y+\cos ^{-1} z=3 \pi$, then
Options:
Solution:
1342 Upvotes
Verified Answer
The correct answer is:
$x+y+z+3=0$
Given,
$\cos ^{-1} x+\cos ^{-1} y+\cos ^{-1} z=3 \pi$
We know that, $\cos ^{-1} x \in[0, \pi]$
$\begin{array}{ll}
\therefore & \cos ^{-1} x=\cos ^{-1} y=\cos ^{-1} z=\pi \\
& x=\cos \pi=-1=y=z \\
& x+y+z+3=0
\end{array}$
Satisfying the equation.
$\cos ^{-1} x+\cos ^{-1} y+\cos ^{-1} z=3 \pi$
We know that, $\cos ^{-1} x \in[0, \pi]$
$\begin{array}{ll}
\therefore & \cos ^{-1} x=\cos ^{-1} y=\cos ^{-1} z=\pi \\
& x=\cos \pi=-1=y=z \\
& x+y+z+3=0
\end{array}$
Satisfying the equation.
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.