Question : If $\cos A=\frac{15}{17}, 0 \leq A \leq 90^{\circ}$, then the value of $\cot(90° - A)$ is:
Option 1: $\frac{8}{15}$
Option 2: $\frac{2 \sqrt{2}}{15}$
Option 3: $\frac{\sqrt{2}}{15}$
Option 4: $\frac{7}{15}$
Correct Answer: $\frac{8}{15}$
Solution :
Given: $\cos A=\frac{15}{17}$
$\sec A=\frac{1}{\cos A}=\frac{17}{15}$
$\cot(90^\circ - A)=\tan A=\sqrt{\sec^2 A-1}$
$=\sqrt{(\frac{17}{15}^2)-1}$
$=\sqrt{\frac{289}{225}-1}$
$=\sqrt{\frac{289-225}{225}}$
$=\sqrt{\frac{64}{225}}$
$=\frac{8}{15}$
Hence, the correct answer is $\frac{8}{15}$.
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