Question : If $\sec A=\frac{17}{15}$, then what is the value of $\cot A$?
Option 1: $\frac{15}{21}$
Option 2: $\frac{15}{7}$
Option 3: $\frac{8}{15}$
Option 4: $\frac{15}{8}$
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Correct Answer: $\frac{15}{8}$
Solution :
Given: $\sec A=\frac{17}{15}$
$⇒\cos A = \frac{15}{17}$
$⇒\sin A = \sqrt{1-\cos^2 A}= \sqrt{1-(\frac{15}{17})^2}$ = $\sqrt{\frac{64}{289}}$ = $\frac{8}{17}$
$\therefore \cot A = \frac{\cos A}{\sin A} = \frac{\frac{15}{17}}{\frac{8}{17}} = \frac{15}{8}$
Hence, the correct answer is $\frac{15}{8}$.
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