Question

Tính : \(A=sin\frac{\Pi}{24}.cos\frac{\Pi}{24}.cos\frac{\Pi}{12}\)

Answer 1

A=\(\frac{1}{2}\left[sin\left(\frac{\pi}{24}-\frac{\pi}{24}\right)+cos\left[\frac{\pi}{24}+\frac{\pi}{24}\right]\right]\).\(cos\frac{\pi}{12}\)

=\(\frac{1}{2}.cos\frac{\pi}{12}.cos\frac{\pi}{12}\)

=\(\frac{1}{2}.\frac{1}{2}\left[cos\left(\frac{\pi}{12}-\frac{\pi}{12}\right)+cos\left(\frac{\pi}{12}+\frac{\pi}{12}\right)\right]\)

=\(\frac{1}{4}.cos\frac{\pi}{6}\)=\(\frac{\sqrt{3}}{8}\)