The value of 1 2 sin /6 . cos /4 - /3 . sec /6 + 5 /412 /2 is equal to?

Answer: Option A

$$\begin{array}{rl}& \frac{1}{\sqrt{2}}\text{sin}\frac{\pi }{6}\text{.cos}\frac{\pi }{4}-\cot \frac{\pi }{3}\text{.sec}\frac{\pi }{6}\text{ + }\frac{5\tan \frac{\pi }{4}}{12\sin \frac{\pi }{2}}\\ & \Rightarrow \frac{1}{\sqrt{2}}\times \frac{1}{2}\times \frac{1}{\sqrt{2}}-\frac{1}{\sqrt{3}}\times \frac{2}{\sqrt{3}}+\frac{5\times 1}{12\times 1}\\ & \Rightarrow \frac{1}{4}-\frac{2}{3}+\frac{5}{12}\\ & \Rightarrow \frac{3-8+5}{12}\\ & \Rightarrow 0\\ & \end{array}$$