If `a^2+b^2=1.`Then `(1+b+ia)/(1+b-ia)=`

If a^(2)+b^(2)=1th en (1+b+ia)/(1+b-ia)=1b.2cb+iad.a+ib

If a^(2)+b^(2)=1 , prove that (1+b+ia)/(1+b-ia)=b+ia .

If A_i= [ [a^i, b^i] , [b^i, a^i]] and if |a|<1, |b|<1 then sum_(i=1)^oo det(A_i) = (A) a^2/(1-a)^2- b^2/(1-b)^2 (B) a^2/(1-a)^2+ b^2/(1-b)^2 (C) a^2/(1+a)^2- b^2/(1+b)^2 (D) (a^2-b^2)/[(1-a^2)(1-b^2)]

If a,b,c are real numbers and z is a complex number such that,a^(2)+b^(2)+c^(2)=1 and b+ic=(1+a)z then (1+iz)/(1-iz) equals.(a) (b-ic)/(1-ia) (b) (a+ib)/(1+c) (c) (1-c)/(a-ib)( d) (1+a)/(b+ic)

If sin^(-1)((2a)/(1+a^2))+sin^(-1)((2b)/(1+b^2))=2tan^(-1)x , then x is equal to [a , b , in (0,1)] (a)(a-b)/(1+a b) (b) b/(1+a b) (c) b/(1+a b) (d) (a+b)/(1-a b)

Prove: |(1,a, b c),(1,b ,c a),(1,c ,a b)|=|(1,a ,a^2),( 1,b,b^2),( 1,c,c^2)|