Question

If cos α= (1+x²)/(1-x²) , x≠ 1 or -1 is it possible or not ? justify your answer.

Answer 1

cosx =(1+x^2)/(1-x^2)

cosx-x^2.cosx =1+x^2

(cosx-1)=x^2(1+cosx)

x^2=(cosx-1)/(1+cosx)

here we see LHS is always positive hence if this equation is correct then RHS must me positive but we know cosx maximum value 1
hence cosx-1 maximum value 0
hence this is possible only when x=0
no solution exist except x=0

hence above ,
cosx=(1+x^2)/(1-x^2)
not possible except x=0