​ If a and b are real numbers such that a^2 + b^2 = 1 then show that a real value of x satisfies the equation, 1 - ix/1+ix = (a - ib)

Question

If a and b are real numbers such that a² + b² = 1 then show that a real value of x satisfies the equation, \(\frac{1-ix}{1+ix}\) = (a - ib)

Answer 1

We have,

Applying componendo and dividendo, we get