Question

If cos A = (1+x²)/(1-x²);
x is not equal to 1 or -1
is it possible or not ?justify your answer

Answer 1

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

=> cosA-x^2.cosA=1+x^2

=>(cosA-1)=x^2 (1+cosA)

=> x^2=(cosA-1)/(cosA+1)


here we see LHS part is always positive term hence RHS is also always positive
but condition is (cosA +1) isn't equal to zero and cosA always greater then 1

this is satisfied when cosA always greater then 1
but we know cosA maximum value 1
hence
cosA=(1+x^2)/(1-x^2) isn't possible .