If 2 ( x2 ) = x^2 + 1x^2 , then the value of ( x - 1/x ) is?

Answer: Option D

$$\begin{array}{rl}& 2\sin \left(\frac{\pi x}{2}\right)=x^2+\frac{1}{x^2}\\ & \text{Let }x=1\\ & \Rightarrow 2\sin 90^{\circ }=1^2+\frac{1}{1^2}\\ & \Rightarrow 2\times 1=1+1\\ & 2=2\left(\text{Matched}\right)\\ & \text{So, }x=1\\ & \Rightarrow \left(x-\frac{1}{x}\right)\\ & \Rightarrow 1-\frac{1}{1}\\ & \Rightarrow 0\end{array}$$