Question : $\triangle\mathrm{ABC}$ is a right angled triangle. $\angle \mathrm{A}=90°$, $AB = 4$ cm, and $BC = 5$ cm. What is the value of $\cos B + \cot C$?
Option 1: $\frac{17}{20}$
Option 2: $\frac{29}{20}$
Option 3: $\frac{23}{20}$
Option 4: $\frac{31}{20}$
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Correct Answer: $\frac{31}{20}$
Solution :
Using the Pythagoras theorem we get,
$AC^2=BC^2-AB^2$
⇒ $AC=\sqrt{5^2-4^2}$
⇒ $AC=3$ cm
Now, $\cos B=\frac{4}{5}$ and $\cot C=\frac{3}{4}$
So, $\cos B + \cot C=\frac{4}{5}+\frac{3}{4}=\frac{31}{20}$
Hence, the correct answer is $\frac{31}{20}$.
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