Question

What will be the value of $\left[\tan \tan (\pi -{\tan }^{-1}z)\right]$?

• A. $-2z$
• B. $-z$
• C. $z$
• D. None of these

Answer 1

The correct option is B $-z$

We have,

$\tan \tan (\pi -{\tan }^{-1}z)$

$\Rightarrow \tan \left[\tan (\pi -{\tan }^{-1}z)\right]$

$\Rightarrow \tan (-{\tan }^{-1}z)[\because \tan (\pi -\theta )=-\tan \theta ]$

$\Rightarrow -tan\left({\tan }^{-1}z\right)[\because \tan (-\theta )=-\tan \theta ]$

$\Rightarrow -z$

Hence, this is the answer.