Question

cosec^–1(cosec x) and cosec (cosec^–1x) are equal functions then maximum range of value of x is-

• A. $\left[ 1 , \frac { \pi } { 2 } \right]$
• B. $\left[ 0 , \frac { \pi } { 2 } \right]$
• C. (–, –1] Č [1, )
• D. [–1, 0) Č [0, 1)

Answer 1

Answer: (A)

$\left[ 1 , \frac { \pi } { 2 } \right]$

Answer 2

cosec (cosec^–1x) = x " x Ī R –(–1, 1)

also range of cosec^–1(cosec x) Ī $\left( 0 , \frac { \pi } { 2 } \right]$

so combining these two.

x Ī $\left[ - \frac { \pi } { 2 } , - 1 \right]$ Č $\left[ 1 , \frac { \pi } { 2 } \right]$