ПОМОГИТЕ!! Тригонометрия! 100 БАЛЛОВ!!

$cos^42a-6\, cos^22a\, sin^22a+sin^42a=\\\\=(cos^22a-sin^22a)^2-4\, cos^22a\, sin^22a=\\\\=(cos4a)^2-(2\, sin2a\, cos2a)^2=cos^24a-sin^24a=\\\\=(cos4a-sin4a)(cos4a+sin4a)=-\sqrt2\, sin(4a-\frac{\pi}{4})\cdot \sqrt2\, cos(4a-\frac{\pi}{4})=\\\\=-sin(8a-\frac{\pi}{2})=sin(\frac{\pi}{2}-8a)=cos8a\; ;\\\\\star \; cosx-sinx=cosx-cos(\frac{\pi}{2}-x)=-2\, sin\frac{\pi}{4}\cdot sin(x-\frac{\pi}{4})=-\sqrt2\, sin(x-\frac{\pi}{4})\; \star$