Question

Sin ET in 1 (-- cos 12 Answer here

Answer 1

`\begin{gathered} \sin (\alpha)\sin (\beta)=(1)/(2)(\cos (\alpha-\beta)-\cos (\alpha+\beta)) \\ In\text{ this case} \\ \alpha=(\pi)/(4) \\ \beta=(\pi)/(6) \\ \alpha+\beta=(\pi)/(4)+(\pi)/(6)=(5\pi)/(12) \\ \alpha-\beta=(\pi)/(4)-(\pi)/(6)=(\pi)/(12) \\ \text{Hence} \\ \sin ((\pi)/(4))\sin ((\pi)/(6))=(1)/(2)(\cos ((\pi)/(12))-\cos ((5\pi)/(12))) \end{gathered}`