Question : If $\cot A=\frac{12}{5}$, then the value of $(\sin A+\cos A) \times \operatorname{cosec} A$ is_____.
Option 1: $\frac{13}{5}$
Option 2: $\frac{17}{5}$
Option 3: $\frac{14}{5}$
Option 4: 1
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Correct Answer: $\frac{17}{5}$
Solution :
Given: $\cot A=\frac{12}{5}$
Now, $(\sin A+\cos A)×\operatorname{cosec}A$
$= (\sin A×\operatorname{cosec}A)+(\cos A×\operatorname{cosec}A)$
$= 1+\cot A$
$= (1+\frac{12}{5})$
$= \frac{17}{5}$
Hence, the correct answer is $\frac{17}{5}$.
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