Question:
If $\sec \theta+\tan \theta=x$, write the value of $\sec \theta-\tan \theta$ in terms of $x .$
Solution:
Given: $\sec \theta+\tan \theta=x$
We know that,
$\sec ^{2} \theta-\tan ^{2} \theta=1$
Therefore,
$\sec ^{2} \theta-\tan ^{2} \theta=1$
$\Rightarrow \quad(\sec \theta+\tan \theta)(\sec \theta-\tan \theta)=1$
$\Rightarrow \quad x(\sec \theta-\tan \theta)=1$
$\Rightarrow \quad(\sec \theta-\tan \theta)=\frac{1}{x}$
Hence, $\sec \theta-\tan \theta=\frac{1}{x}$
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