If 2x = sin θ and 2/x=cosθ then the value of 4(x^2+1/(x^2)) is :

Given :-

2x = sin θ &   \(\frac{2  }{x}\) = cosθ 

Squaring both sides

4x² = sin²θ    -----(1)

\(\frac{4  }{x²}\) = cos²θ      ----(2)

Adding equation 1 and 2.

sin²θ + cos²θ = 4x² + \(\frac{4  }{x²}\) 

{ sin²θ + cos²θ  = 1 }

1 = 4x² + \(\frac{4  }{x²}\)

Ans :- 1