Question : If $\cot B=9 $, then what will be the value of $\sec ^2 B$?
Option 1: $\frac{98}{81}$
Option 2: $\frac{92}{81}$
Option 3: $\frac{42}{81}$
Option 4: $\frac{82}{81}$
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Correct Answer: $\frac{82}{81}$
Solution :
Given, $\cot B=9 $
⇒ $\frac{1}{\tan B}=9$
⇒ $\tan B = \frac{1}{9}$
⇒ $\tan^2 B = \frac{1}{81}$
⇒ $\sec^2 B-1 = \frac{1}{81}$
⇒ $\sec^2 B = \frac{82}{81}$
Hence, the correct answer is $ \frac{82}{81}$.
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