If $$\tan\frac{A}{2}=x$$, then the value of x is

Given : $$tan(\frac{A}{2})=x$$

Using double angle formula, $$tan(A)=\frac{2x}{1-x^2}$$

=> $$tan^2(A)=\frac{4x^2}{1-2x^2+x^4}$$

Also, $$sec^2(A)=1+tan^2(A)$$

=> $$sec^2(A)=1+(\frac{4x^2}{1-2x^2+x^4})$$

=> $$sec^2(A)=\frac{(1-2x^2+x^4)+(4x^2)}{1-2x^2+x^4}$$

=> $$sec^2(A)=\frac{1+2x^2+x^4}{1-2x^2+x^4}$$

=> $$sec^2(A)=(\frac{1+x^2}{1-x^2})^2$$

=> $$sec(A)=\frac{1+x^2}{1-x^2}$$

=> $$cos(A)=\frac{1-x^2}{1+x^2}$$

=> $$cos(A)+x^2cos(A)=1-x^2$$

=> $$x^2[1+cos(A)]=1-cos(A)$$

=> $$x=\sqrt{\frac{1-cos(A)}{1+cos(A)}}$$

=> Ans - (D)