Известно, что sin (π/3+t) + sin (π/3-t) = p. Найдите sin (π/3+t) * sin (π/3-t)

Sin (π/3 + t) + sin (π/3 - t) = 2 sin (π/3) ·cos t = 2·√3/2·cos t = √3·cos t = p

cos t = p / √3

cos 2t = 2cos²t - 1 = 2·p²/3 - 1

sin (π/3 + t) · sin (π/3 - t) = 1/2 (cos 2t - cos (2π/3)) = 1/2 · cos 2t - 1/2 · (-1/2) =

= 1/2 cos 2t + 1/4 = 1/2 · (2·p²/3 - 1) + 1/4 = p²/3 - 3/4