If $\tan ^{-1} \frac{x-1}{x-2}+\tan ^{-1} \frac{x+1}{x+2}=\frac{\pi}{4}$, then $x=$

JEE MATHEMATICS MCQ: INVERSE TRIGONOMETRY

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Application +4 | -1

\tan ^{-1} \frac{x-1}{x-2}+\tan ^{-1} \frac{x+1}{x+2}=\frac{\pi}{4}

, then

x=

View answer and explanation

Correct option: C

\pm \frac{1}{\sqrt{2}}

Option C (

\pm \frac{{1}}{{\sqrt{{2}}}}

) is correct because it is obtained by applying the tangent addition formula and solving the resulting quadratic equation.

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