Question

sin^4(π/12) - cos^4(π/12)

Answer 1

$sin^4\frac{\pi}{12}-cos^4\frac{\pi}{12}=(sin^2\frac{\pi}{12}-cos^2\frac{\pi}{12})(sin^2\frac{\pi}{12}+cos^2\frac{\pi}{12})=\\\\=-(cos^2\frac{\pi}{12}-sin^2\frac{\pi}{12})=-cos\frac{\pi}{6}=-\frac{\sqrt3}{2}$