Question : If $\sec\theta +\tan\theta = 3$, then what is the value of $\sec \theta-\tan \theta$?
Option 1: $\frac{1}{3}$
Option 2: $6$
Option 3: $\frac{1}{6}$
Option 4: $\frac{1}{5}$
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Correct Answer: $\frac{1}{3}$
Solution :
Given, $\sec\theta +\tan\theta = 3$
We know that,
$\sec^2θ−\tan^2θ=1$
⇒ $(\secθ−\tanθ)(\secθ+\tanθ)=1$
⇒ $(\secθ−\tanθ)(3)=1$
⇒ $\secθ-\tanθ=\frac13$
Hence, the correct answer is $\frac{1}{3}$.
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