MCQ
Write the function in the simplest form: $\tan ^{-1}\left(\frac{1}{\sqrt{x^{2}-1}}\right),|x|>1$
- ✓$\frac{\pi}{2}-\sec ^{-1} x $
- B$\frac{\pi}{2}+\sec ^{-1} x $
- C$\frac{\pi}{2} + cosec ^{-1} x $
- D$\frac{\pi}{2}-cosec ^{-1} x $
Put $x=cosec \theta \Rightarrow \theta=cosec^{-1} x$
$\therefore \tan ^{-1} \frac{1}{\sqrt{x^{2}-1}}$
$=\tan ^{-1} \frac{1}{\sqrt{\cos e c^{2} \theta-1}}$
$=\tan ^{-1}\left(\frac{1}{\cot \theta}\right)$
$=\tan ^{-1}(\tan \theta)$
$=\theta$
$=cosec ^{-1} x$
$=\frac{\pi}{2}-\sec ^{-1} x $ $\left[A s, \cos e c^{-1} x+\sec ^{-1} x=\frac{\pi}{2}\right]$
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Statement $-1 :$ The probability that the chosen numbers when arranged in some order will form an $A.P.$ is $\frac{1}{{85}}$ .
Statement $-2 :$ If the four chosen numbers form an $A.P.$, then the set of all possible values of common difference is $\left( { \pm 1, \pm 2, \pm 3, \pm 4, \pm 5} \right)$ છે.
${L_1}:\bar r = \hat i + \hat j + \lambda \left( {\hat i + \hat j - \hat k} \right)$
${L_2}:\bar r = \hat j + \hat k + \mu \left( {\hat j + 2\hat k - \hat i} \right)$ equal to