JEE Mains · Maths · STD 11 - 8. sequence and series
If \(x,y,z\) are in \(A.P.\) and \({\tan ^{ - 1}}x,{\tan ^{ - 1}}y\) and \({\tan ^{ - 1}}z\) are also in other \(A.P.\) then . . .
- A \(x = y = z\)
- B \(x = y = - z\)
- C \(x = 1;y = 2;z = 3\)
- D \(x = 2;y = 4;z = 6\)
Answer & Solution
Correct Answer
(A) \(x = y = z\)
Step-by-step Solution
Detailed explanation
\(2 y=x+z\) ....\((1)\) As \(\tan ^{-1} x, \tan ^{-1} y, \tan ^{-1} z\) in \(A.P\) \(\Rightarrow 2 \tan ^{-1} y=\tan ^{-1} \frac{x+z}{1-x z}\) \(\frac{2 y}{1-y^{2}}=\frac{x+z}{1-x z}\) \(\frac{x-z}{1-y^{2}}=\frac{x+z}{1-x z}\) by \(( 1)\)…
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