Question : The value of $\text{cosec}^{2}\: 18°-\frac{1}{\cot^{2}72°}$ is:
Option 1: $\frac{1}{\sqrt3}$
Option 2: $\frac{\sqrt2}{3}$
Option 3: $\frac{1}{2}$
Option 4: $1$
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Correct Answer: $1$
Solution :
$\text{cosec}^{2}\: 18°-\frac{1}{\cot^{2}72°}$
$= \text{cosec}^{2}\: 18° - \frac{1}{\cot^{2}(90-18)°}$
$= \text{cosec}^{2}\: 18° - \frac{1}{\tan^{2}18°}$
$= \text{cosec}^{2}\: 18° - \cot^{2}18°$
$= 1$
Hence, the correct answer is $1$.
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