Question : If $\tan \theta=\frac{4}{5}$, then $\sec \theta$ is:
Option 1: $\frac{\sqrt{41}}{5}$
Option 2: $\frac{\sqrt{41}}{4}$
Option 3: $\frac{5}{4}$
Option 4: $\frac{\sqrt{41}}{20}$
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Correct Answer: $\frac{\sqrt{41}}{5}$
Solution :
Given: $\tan \theta=\frac{4}{5}$
We know, $\sec^2 \theta-\tan^2 \theta=1$
$⇒\sec^2 \theta-\frac{16}{25}=1$
$⇒\sec^2 \theta=\frac{41}{25}$
$\therefore\sec \theta=\frac{\sqrt{41}}{5}$
Hence, the correct answer is $\frac{\sqrt{41}}{5}$.
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