15. cos²(π/3) − sin²(π/4) + ctg(π/6) · tg(π/3)

Подставим значения: \(\cos\frac{\pi}{3}=\frac12\), \(\sin\frac{\pi}{4}=\frac{\sqrt2}{2}\), \(\ctg\frac{\pi}{6}=\sqrt3\), \( g\frac{\pi}{3}=\sqrt3\).

\(\left(\frac12\right)^2-\left(\frac{\sqrt2}{2}\right)^2+\sqrt3\cdot\sqrt3=\frac14-\frac12+3=\frac{11}{4}.\)

Ответ: \(\frac{11}{4}\).