Question : If $A$ is an acute angle and $8\sec A=17$, find the value of $\tan A$.
Option 1: $\frac{15}{17}$
Option 2: $\frac{15}{8}$
Option 3: $\frac{8}{15}$
Option 4: $\frac{8}{17}$
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Correct Answer: $\frac{15}{8}$
Solution :
Given, $8\sec A=17$
⇒ $\sec A=\frac{17}{8}$
We know, $\tan^2 A=\sec^2 A-1$
⇒ $\tan^2 A=(\frac{17}{8})^2-1$
⇒ $\tan^2 A=\frac{225}{64}$
⇒ $\tan A=\frac{15}{8}$
Hence, the correct answer is $\frac{15}{8}$.
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