Question : If $\tan \alpha = 6$, then $\sec \alpha$ is equal to:
Option 1: $\sqrt{7}$
Option 2: $\sqrt{5}$
Option 3: $\sqrt{37}$
Option 4: $\sqrt{35}$
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Answer (1)
11th Jan, 2024
Correct Answer: $\sqrt{37}$
Solution :
Given:
$\tan \alpha=6$
We know,
$\sec^2 \alpha-\tan^2 \alpha=1$
⇒ $\sec^2 \alpha-6^2=1$
⇒ $\sec^2 \alpha=36+1$
$\therefore \sec \alpha=\sqrt{37}$
Hence, the correct answer is $\sqrt{37}$.
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