(2sin^2 4a-1)/(2ctg (П/4+4a)cos^2(5П/4-4a))

[latex]\frac{2sin^24a-1}{2ctg(\frac{\pi}{4}+4a)cos^2(\frac{5\pi}{4}-4a)}=-1[/latex] Числитель: [latex]2sin^24a-1 = -cos8a[/latex]  Знаменатель: [latex]2ctg(\frac{\pi}{4}+4a)cos^2(\frac{5\pi}{4}-4a)=2\frac{cos(\frac{\pi}{4}+4a)cos^2(\pi+\frac{\pi}{4}-4a)}{sin(\frac{\pi}{4}+4a)}=[/latex] [latex]2cos(\frac{\frac{\pi}{2}+8a}{2})cos(\frac{\frac{\pi}{2}-8a}{2})\frac{cos(\frac{\pi}{4}-4a)}{sin(\frac{\pi}{4}+4a)}=[/latex][latex](cos\frac{\pi}{2}+cos8a)\frac{cos\frac{\pi}{4}cos4a+sin\frac{\pi}{4}sin4a}{sin\frac{\pi}{4}cos4a+cos\frac{\pi}{4}sin4a}=\frac{cos8a(sin4a+cos4a)}{sin4a+cos4a}=cos8a[/latex] [latex]\frac{-cos8a}{cos8a}=-1[/latex]