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TS EAMCET · Maths · Inverse Trigonometric Functions

If \(\cos ^{-1} x+\cos ^{-1} y+\cos ^{-1} z=3 \pi\), then

  1. A \(x+y+z-3=0\)
  2. B \(x+y+z+3=0\)
  3. C \(x+2 y+3 z-5=0\)
  4. D \(x-y-z=0\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(x+y+z+3=0\)

Step-by-step Solution

Detailed explanation

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.