Question : If $\sec \theta+\tan \theta=4$, then $\sec \theta-\tan \theta=$___________.
Option 1: $\frac{1}{4}$
Option 2: $\frac{1}{2}$
Option 3: 2
Option 4: 4
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Correct Answer: $\frac{1}{4}$
Solution :
Given, $\sec \theta+\tan \theta=4$
We know that, $\sec^2\theta-\tan^2\theta = 1$
⇒ $(\sec\theta-\tan\theta)(\sec\theta+\tan\theta)=1$
⇒ $(\sec\theta-\tan\theta)(4)=1$
$\therefore\sec\theta-\tan\theta=\frac{1}{4}$
Hence, the correct answer is $\frac{1}{4}$.
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