Question : The value of $\operatorname{cosec} 30^{\circ}-\cos 60^{\circ}$ is:
Option 1: $1$
Option 2: $\frac{1}{2}$
Option 3: $\frac{3}{2}$
Option 4: $\frac{2 \sqrt{2}-1}{\sqrt{2}}$
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Correct Answer: $\frac{3}{2}$
Solution :
$\operatorname{cosec} 30^{\circ}=2$
And $\cos 60^{\circ}=\frac{1}{2}$
So, $\operatorname{cosec} 30^{\circ}-\cos 60^{\circ} = 2 - \frac{1}{2}=\frac{3}{2}$
Hence, the correct answer is $\frac{3}{2}$.
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