If \(2\cot A = 4\), find the value of \(\dfrac{\text{cosec}^2A + 1}{\text{cosec}^2A - 1}\).
1.5
\(2\cot A=4 \Rightarrow \cot A=2\).
Using the identity \(\text{cosec}^2A = 1+\cot^2A = 1+4 = 5\).
Substituting: \(\dfrac{5+1}{5-1} = \dfrac{6}{4} = 1.5\).
Hence, the value of the expression is 1.5.
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