Question : If $\sin\phi=\frac{5}{6}$, the value of $\cot\phi \cdot \sin\phi \cdot \cos\phi$ is:
Option 1: $\frac{6}{5}$
Option 2: $\frac{25}{36}$
Option 3: $\frac{5}{6}$
Option 4: $\frac{11}{36}$
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Correct Answer: $\frac{11}{36}$
Solution :
Given: $\sin\phi=\frac{5}{6}$.
Now, $\cot\phi \cdot \sin\phi \cdot \cos\phi$
= $\frac{\cos\phi}{\sin\phi}×\sin\phi×\cos\phi$
= $\cos^2\phi$
= $1–\sin^2\phi$
= $1–(\frac{5}{6})^2$
= $1–\frac{25}{36}$
= $\frac{11}{36}$
Hence, the correct answer is $\frac{11}{36}$.
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