Question

Помогите с алгеброй, пожалуйста

Answer 1

$sin(frac{pi}{3}+t)+sin(frac{pi}{3}-t)=2sin(frac{(frac{pi}{3}+t)+(frac{pi}{3}-t)}{2})*cos(frac{(frac{pi}{3}+t)-(frac{pi}{3}-t)}{2})=\=2sinfrac{pi}{3}*cost=2*frac{sqrt{3}}{2}*cost=boxed{sqrt{3}cost=p}$
$boxed{cost=frac{p}{sqrt{3}}}$


$sin(frac{pi}{3}+t)*sin(frac{pi}{3}-t)=\=frac{1}{2}(cos((frac{pi}{3}+t)-(frac{pi}{3}-t))-cos((frac{pi}{3}+t)+(frac{pi}{3}-t)))=\=frac{1}{2}(cos2t-cosfrac{2pi}{3})=frac{1}{2}((2cos^2t-1)-(-frac{1}{2}))=cos^2t-frac{1}{2}+frac{1}{4}=\=cos^2t-frac{1}{4}=(frac{p}{sqrt{3}})^2-frac{1}{4}=frac{p^2}{3}-frac{1}{4}=frac{4p^2-3}{12}$