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The value of $x$ that satisfies $\tan^{- 1} (\tan 3) = \tan^{2} x$ , is

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π3

−π3

tan−1⁡3

none of these

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Correct option is D

We have,tan−1⁡(tan⁡3)=tan−1⁡{tan⁡(3−π)}=3−π<0and, tan2⁡x≥0 ∴ tan−1⁡(tan⁡3)=tan2⁡x has no solution.

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The value of x that satisfies tan−1⁡(tan⁡3)=tan2⁡x, is

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The value of $x$ that satisfies $\tan^{- 1} (\tan 3) = \tan^{2} x$ , is