Помогите с алгеброй, пожалуйста

Решите задачу:

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

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