Q51 / 150 · MHT CET 2026 (11 April Shift 1) · Mathematics

The value of the expression $\tan(x - 9\pi)$ is equal to:

  • A
    $-\tan x$
  • B
    $-\cot x$
  • Correct answer
    C
    $\tan x$
  • D
    $\cot x$

Solution

$\tan(x - 9\pi) = -\tan(9\pi - x)$

$-\tan(9\pi - x) = -\tan(4(2\pi) + \pi - x)$

Using the periodic property $\tan(2n\pi + \theta) = \tan \theta$ for integer $n$:

$-\tan(4(2\pi) + \pi - x) = -\tan(\pi - x)$

Since $\tan(\pi - \theta) = -\tan \theta$:

$-\tan(\pi - x) = -(-\tan x) = \tan x$

Hence, the correct answer is option: 'C'.

Relevant Questions