Question

If $3x=\sec \theta ,\frac{3}{x}=\tan \theta$, then find the value of $x^2-\frac{1}{x^2}$

Answer 1

Given $3x=\sec \theta ,\frac{3}{x}=\tan \theta$

As we know that

${\text{sec}}^2\theta -{\tan }^2\theta =1$

On putting the value of $\sec \theta$ and $\tan \theta$ in the above equation, we have

$\Rightarrow (3x{)}^2-(\frac{3}{x}{)}^2=1$

$\Rightarrow 9x^2-\frac{9}{x^2}=1$

$\Rightarrow 9(x^2-\frac{1}{x^2})=1$

$\therefore x^2-\frac{1}{x^2}=\frac{1}{9}$