TS EAMCET · Maths · Inverse Trigonometric Functions
If \(\cos ^{-1} x+\cos ^{-1} y+\cos ^{-1} z=3 \pi\), then
- A \(x+y+z-3=0\)
- B \(x+y+z+3=0\)
- C \(x+2 y+3 z-5=0\)
- D \(x-y-z=0\)
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.
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