If 4x = sec θ and 4/x = tan θ then $$(x^2 - \frac{1}{x^2})$$ is
$$4x = sec θ$$
$$x = \frac{sec θ}{4}$$
$$x^2 = \frac{sec^2 θ}{16}$$
$$\frac{4}{x} = tan θ$$
$$\frac{1}{x} = \frac{tan θ}{4} $$
$$\frac{1}{x^2} = \frac{tan^2 θ}{16} $$
$$ x^2 - \frac{1}{x^2} = \frac{sec^2 θ}{16} - \frac{tan^2 θ}{16} $$
$$ x^2 - \frac{1}{x^2} = \frac{sec^2 θ - tan^2 θ}{16}$$
$$sec^2 θ - tan^2 θ =1$$
$$ x^2 - \frac{1}{x^2} = \frac{1}{16}$$
Hence Option A is the correct answer
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