A value of x for which ( ⁻¹(1+x) )= ( ⁻¹ x ) , is :

Step-by-step solution

( ⁻¹(1+x) )= ( ⁻¹ x ) aligned & cosec ^2 ( ⁻¹(1+x) )= ^2 ( ⁻¹ x ) & 1+ [ ( ⁻¹(1+x) ) ]^2 & =1+ [ ( ⁻¹ x ) ]^2 & (1+x)^2=x^2 x=- 1 2 aligned