First slide

Properties of ITF

Question

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

Moderate

A

$\frac{π}{3}$
B

$- \frac{π}{3}$
C

$\sqrt{\tan^{- 1} 3}$
D

none of these

Solution

We have,
$\tan^{- 1} (\tan 3) = \tan^{- 1} {\tan (3 - π)} = 3 - π < 0$
and, $\tan^{2} x \geq 0$
$∴ \tan^{- 1} (\tan 3) = \tan^{2} x$ has no solution.

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