Question

If $5x=\sec \theta$ and $\frac{5}{x}=\tan \theta$ , find the value of $5(x^2-\frac{1}{x^2})$

Answer 1

$\Rightarrow 5x=sec\theta$ and $\frac{5}{x}=tan\theta$

then $5(x^2-\frac{1}{x^2})=\frac{25}{5}(x^2-\frac{1}{x^2})$

$\Rightarrow \frac{1}{5}(25x^2-\frac{25}{x^2})$

$\Rightarrow \frac{1}{5}(se{c}^2\theta -ta{n}^2\theta )$

$\Rightarrow \frac{1}{5}(\frac{1}{co{s}^2\theta }-\frac{si{n}^2\theta }{co{s}^2\theta })=\frac{1}{5}\left[\frac{1-si{n}^2\theta }{co{s}^2\theta }\right]$

$\Rightarrow \frac{1}{5}\left(\frac{co{s}^2\theta }{co{s}^2\theta }\right)=\frac{1}{5}$