If `a`, `b` are real and `a^2+b^2=1`, then show that the equation `(sqrt(1+x)-isqrt(1-x))/(sqrt(1+x)+isqrt(1-x))=a-ib` is satisfied y a real value of `x`.

Explanation

let x e real

`(sqrt(1+x)-isqrt(1-x))/(sqrt(1+x)+isqrt(1-x))`

`{(sqrt(1+x)-isqrt(1-x))/((a+x)+(1-x))}`

`(1+x-1_x-2isqrt(1-x^2))/2`

`(2x-2isqrt(1-x^2))/2`

`x-isqrt(1-x^2)`

`a=x`

`b=sqrt(1-x^2)`

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