Question

The value of $\sin {30}^{\circ }\cdot \sin {45}^{\circ }\cdot \text{cosec}{45}^{\circ }\cdot \cos {30}^{\circ }$ is ___

• A. $\sqrt{3}$
• B. $\frac{1}{\sqrt{3}}$
• C. $\frac{\sqrt{3}}{2}$
• D. $\frac{\sqrt{3}}{4}$

Answer 1

The correct option is D $\frac{\sqrt{3}}{4}$

The value of $\sin {30}^0.\sin {45}^0.\text{cosec}{45}^0.\cos {30}^0$is

$=\frac{1}{2}\times \frac{1}{\sqrt{2}}\times \sqrt{2}\times \frac{\sqrt{3}}{2}$

$=\frac{\sqrt{3}}{4}$