Question : Find the value of $\sec\theta - \tan\theta$, if $\sec\theta + \tan\theta = \sqrt{5}$.
Option 1: $5$
Option 2: $5 \frac{1}{5}$
Option 3: $\frac{\sqrt{5}}{5}$
Option 4: $\sqrt{5}$
Correct Answer: $\frac{\sqrt{5}}{5}$
Solution :
Given: $\sec\theta + \tan\theta = \sqrt{5}$
To find the value of $\sec\theta - \tan\theta$
We know,
$\sec^2\theta -\tan^2\theta = 1$
⇒ $\sec\theta -\tan\theta=\frac{1}{\sec\theta + \tan\theta}$
So, $\sec\theta - \tan\theta = \frac{1}{\sqrt{5}} = \frac{\sqrt{5}}{5}$
Hence, the correct answer is $\frac{\sqrt5}{5}$.
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