Question : If $\tan A=\frac{5}{12}$, then the value of $\cos A=$______.
Option 1: $\frac{12}{5}$
Option 2: $\frac{13}{5}$
Option 3: $\frac{5}{13}$
Option 4: $\frac{12}{13}$
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Correct Answer: $\frac{12}{13}$
Solution :
Given: $\tan A = \frac{5}{12}$
Then, $\sec A$
= $\sqrt{(1 + \tan^2A)}$
= $\sqrt{(1 + \frac{25}{144})}$
= $\sqrt{(\frac{169}{144})}$
= $\frac{13}{12}$
So, $\cos A = \frac{1}{\sec A}=\frac{12}{13}$
Hence, the correct answer is $\frac{12}{13}$.
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