Question

известно ,что sin(п/6+t)+sin)п/6-t=p.Найдите sin(п/6+t)sin(п/6-t)СРОЧНО!

Answer 1

$sinleft(dfrac{pi}{6}+tright)+sinleft(dfrac{pi}{6}-tright)=2sindfrac{dfrac{pi}{6}+t+dfrac{pi}{6}-t}{2}cosdfrac{dfrac{pi}{6}+t-dfrac{pi}{6}+t}{2}=\ \ =2sindfrac{pi}{6}cos t=2cdotdfrac{1}{2}cos t=cos t;~~~~~boxed{cos t=p}$

$sinleft(dfrac{pi}{6}+tright)sinleft(dfrac{pi}{6}-tright)=dfrac{cosleft(dfrac{pi}{6}+t-dfrac{pi}{6}+tright)-cosleft(dfrac{pi}{6}+t+dfrac{pi}{6}-tright)}{2}=\ \ \ =dfrac{cos2t-cosdfrac{pi}{3}}{2}=dfrac{cos2t-dfrac{1}{2}}{2}=dfrac{2cos2t-1}{4}=dfrac{2(2cos^2t-1)-1}{4}=\ \ \ =dfrac{4cos^2t-2-1}{4}=dfrac{4cos^2t-3}{4}=boxed{dfrac{4p^2-3}{4}}$