Question

Чему равен sin п/12????

Answer 1

$sindfrac{pi}{12}=sin bigg(dfrac{pi}{3}-dfrac{pi}{4}bigg)=sindfrac{pi}{3}cosdfrac{pi}{4}-cosdfrac{pi}{3}sindfrac{pi}{4}=dfrac{sqrt{3}}{2}cdotdfrac{1}{sqrt{2}}-dfrac{1}{2}cdotdfrac{1}{sqrt{2}}=\ \ \ =dfrac{1}{sqrt{2}}cdot bigg(dfrac{sqrt{3}}{2}-dfrac{1}{2}bigg)=dfrac{sqrt{3}-1}{2sqrt{2}}$

Ответ: $dfrac{sqrt{3}-1}{2sqrt{2}}$