Question

$\tan |x|=|\tan x|$ if

• A. $x\in \left(-\frac{2k+1}{2}\pi ,-k\pi \right)$
• B. $x\in \left(k\pi ,\frac{2k+1}{2}\pi \right)$
• C. $x\in \left(\frac{2k+1}{2}\pi ,k\pi \right)$
• D. $x\in \left(-k\pi ,-\pi \frac{2k-1}{2}\right)$

Answer 1

Answer: (A)

$|tanx|$ is always positive
$\Rightarrow \tan |x|>0\Rightarrow |x|$ lies in either $I$ or $III$ quadrant
By verification only (1) satisfy these conditions
Where $k\in Z$