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Question: Answered & Verified by Expert
If $\cos ^{-1} x+\cos ^{-1} y+\cos ^{-1} z=3 \pi$, then
MathematicsInverse Trigonometric FunctionsTS EAMCETTS EAMCET 2019 (04 May Shift 2)
Options:
  • A $x+y+z-3=0$
  • B $x+y+z+3=0$
  • C $x+2 y+3 z-5=0$
  • D $x-y-z=0$
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.

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