Question

Sa se calculeze:

$cos \ \frac{23 \pi}{12}* sin \ \frac{\pi}{12}$

Answer 1

$\cos \frac{23\pi}{12}=\cos \frac{24\pi-\pi}{12}=\cos(2\pi- \frac{\pi}{12})=\cos(- \frac{\pi}{12})=\cos \frac{\pi}{12}$

Calculul devine
$sin \frac{\pi}{12}\cos \frac{\pi}{12} \\ \hbox{De aici posibil sa o dau in bara, sunt prea adormit:} \\ Stim\ ca\ \sin2x=2\sin x\cos x \\ Deci\ inmultim\ si\ impartim\ cu\ 2: \\ \frac{2sin \frac{\pi}{12} cos \frac{\pi}{12} }{2}= \frac{sin2\cdot \frac{\pi}{12} }{2}= \frac{sin \frac{\pi}{6} }{2}= \\ \frac{ \frac{1}{2} }{2} = \frac{1}{4}$