Question : If $3 \operatorname{cosec} A=7$, then what is the value of $\cos A \tan A$?
Option 1: $\frac{2 \sqrt{10}}{7}$
Option 2: $\frac{3}{7}$
Option 3: $\frac{4}{7}$
Option 4: $\frac{\sqrt{10}}{7}$
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Correct Answer: $\frac{3}{7}$
Solution :
Given: $3 \operatorname{cosec} A=7$
⇒ $\operatorname{cosec} A=\frac{7}{3}$
⇒ $\frac{1}{\sin A}=\frac{7}{3}$
⇒ $\sin A=\frac{3}{7}$
$\therefore$ $\cos A \tan A=\cos A\times\frac{\sin A}{\cos A}=\sin A=\frac{3}{7}$
Hence, the correct answer is $\frac{3}{7}$.
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