Вычислите:
\( \frac{sin^2\frac{\pi}{5}*cos^2\frac{\pi}{5}}{1-cos^4\frac{2\pi}{5}-cos^2\frac{2\pi}{5}sin^2\frac{2\pi}{5}}= \)
Решение
\( \frac{sin^2\frac{\pi}{5}*cos^2\frac{\pi}{5}}{1-cos^2\frac{2\pi}{5}(cos^2\frac{2\pi}{5}+sin^2\frac{2\pi}{5})}= \)
\( =\frac{0,25sin^2\frac{2\pi}{5}}{sin^2\frac{2\pi}{5}}=0,25 \)
Ответ: 0,25