Question

tan-1 1 / √x2 - 1 ,|x| > 1

Answer 1

Answer:

okkkkkkjjjkkuhhkkkkk

Answer 2

Answer:

Step-by-step explanation:

माना   $cosec^{-1} x=\theta,  x= cosec\theta$

$\theta = [-\dfrac{\pi}{2} ,\dfrac{\pi}{2} ]-\{0\}$

लेकिन   |x| > 1 ; $|cosec\theta|>1$

⇒$\theta = [-\dfrac{\pi}{2} ,\dfrac{\pi}{2} ]-\{0\}$

अब

    $tan^{-1}(\dfrac{1}{\sqrt{x^2-1} } )\\\\\\=tan^{-1}(\dfrac{1}{\sqrt{cosec^2\theta-1} })\\\\\\=tan^{-1}(\dfrac{1}{|cot\theta|} )\\\\\\=tan^{-1}(|tan\theta|)\\\\\\=\left \{ {{tan^{-1}(tan\theta) ; 0<\theta<\pi/2} \atop {tan^{-1}(-tan\theta);-\pi/2<\theta<0}} \right. \\\\\\=\left \{ {{cosec^{-1}x ; x>1} \atop {-cosec^{-1}x; x<-1}} \right.$