Question

[1-{1-(1-x^2) ^-1}^-1]^-1/2​

Answer 1

Simplified value = x

Step-by-step explanation:

$[ 1 - (1 - ( { \: {1 - {x}^{2} )}^{ - 1} )}^{ - 1} {]}^{ \frac{ - 1}{2} } \\ = </p><p>[ 1 - (1 - { \: \frac{1}{1 - {x}^{2} } )}^{ - 1} {]}^{ \frac{ - 1}{2} }</p><p></p><p>$

$[ 1 - ( { \: \frac{1 - {x}^{2} - 1}{1 - {x}^{2} } )}^{ - 1} {]}^{ \frac{ - 1}{2} }$

$[ 1 - ( { \: \frac{ - {x}^{2} }{1 - {x}^{2} } )}^{ - 1} {]}^{ \frac{ - 1}{2} }$

$[ 1 - ( { \: \frac{1 - {x}^{2} }{ - {x}^{2} } )} {]}^{ \frac{ - 1}{2} }$

$[ 1 + ( { \: \frac{1 - {x}^{2} }{ {x}^{2} } )} {]}^{ \frac{ - 1}{2} }$

$[ { \: \frac{ {x}^{2} + 1 - {x}^{2} }{ {x}^{2} } } {]}^{ \frac{ - 1}{2} }$

$[ { \: \frac{ 1 }{ {x}^{2} } } {]}^{ \frac{ - 1}{2} }$

$[ { {x}^{ - 2} } {]}^{ \frac{ - 1}{2} }$

${x}^{ - 2 \times \frac{ - 1}{2} }$

${ x}^{1}$

= x

Hence, the answer is = x.