Question

Тригонометрия 9 класс
Будьте добры

Answer 1

$\cos{4\alpha}$

Объяснение:

$ctg(4\alpha-\pi)(\cos^4(\frac{5}{4}\pi-2\alpha )-\sin^4(\frac{9}{4}\pi-2\alpha))=\\ \\=ctg{4\alpha}\cdot (\cos^4(\pi+\frac{1}{4}\pi-2\alpha )-\sin^4(2\pi+\frac{1}{4}\pi-2\alpha))=\\ \\ =ctg{4\alpha}\cdot (\cos^4(\frac{1}{4}\pi-2\alpha )-\sin^4(\frac{1}{4}\pi-2\alpha))=\\ \\=ctg{4\alpha}\cdot ((\cos^2(\frac{1}{4}\pi-2\alpha ))^2-(\sin^2(\frac{1}{4}\pi-2\alpha))^2)=\\\\$

$=ctg{4\alpha}\cdot (\cos^2(\frac{1}{4}\pi-2\alpha )-\sin^2(\frac{1}{4}\pi-2\alpha ))\cdot(\cos^2(\frac{1}{4}\pi-2\alpha )+\sin^2(\frac{1}{4}\pi-2\alpha ))=\\ \\=ctg{4\alpha}\cdot \cos{(2\cdot(\frac{1}{4}\pi-2\alpha ))}\cdot 1=ctg{4\alpha}\cdot \cos{(\frac{\pi}{2}-4\alpha )}=\frac{\cos{4\alpha}}{\sin{4\alpha}}\cdot \sin{4\alpha}=\cos{4\alpha}$