![\frac{1+tg^{2}x }{4Sin^{2}x }=1\\\\\frac{\frac{1}{Cos^{2}x }}{4Sin^{2}x }=1\\\\\frac{1}{4Sin^{2}x Cos^{2}x}=1\\\\4Sin^{2}x Cos^{2}x=1\\\\Sin^{2}2x=1](https://tex.z-dn.net/?f=%5Cfrac%7B1%2Btg%5E%7B2%7Dx+%7D%7B4Sin%5E%7B2%7Dx+%7D%3D1%5C%5C%5C%5C%5Cfrac%7B%5Cfrac%7B1%7D%7BCos%5E%7B2%7Dx+%7D%7D%7B4Sin%5E%7B2%7Dx+%7D%3D1%5C%5C%5C%5C%5Cfrac%7B1%7D%7B4Sin%5E%7B2%7Dx+Cos%5E%7B2%7Dx%7D%3D1%5C%5C%5C%5C4Sin%5E%7B2%7Dx+Cos%5E%7B2%7Dx%3D1%5C%5C%5C%5CSin%5E%7B2%7D2x%3D1)
![1)Sin2x=1\\\\2x=\frac{\pi }{2}+2\pi n,n\in z\\\\x=\frac{\pi }{4}+\pi n,n\in z\\\\2)Sin2x=-1\\\\2x=-\frac{\pi }{2}+2\pi n,n\in z\\\\x=-\frac{\pi }{4} +\pi n,n\in z](https://tex.z-dn.net/?f=1%29Sin2x%3D1%5C%5C%5C%5C2x%3D%5Cfrac%7B%5Cpi+%7D%7B2%7D%2B2%5Cpi+n%2Cn%5Cin+z%5C%5C%5C%5Cx%3D%5Cfrac%7B%5Cpi+%7D%7B4%7D%2B%5Cpi+n%2Cn%5Cin+z%5C%5C%5C%5C2%29Sin2x%3D-1%5C%5C%5C%5C2x%3D-%5Cfrac%7B%5Cpi+%7D%7B2%7D%2B2%5Cpi+n%2Cn%5Cin+z%5C%5C%5C%5Cx%3D-%5Cfrac%7B%5Cpi+%7D%7B4%7D+%2B%5Cpi+n%2Cn%5Cin+z)
Эти два ответа можно объединить :
![x=\frac{\pi }{4}+\frac{\pi n }{2},n\in z](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B%5Cpi+%7D%7B4%7D%2B%5Cfrac%7B%5Cpi+n+%7D%7B2%7D%2Cn%5Cin+z)
Четных цифр, отличных от 0 всего 4:
2;4;6;8.
Первое место можно заполнить четырьмя способами, второе место тремя, третье - двумя.
Всего 4·3·2=24 способами, значит 24 числа:
246;
264;
248;
284;
268;
286;
462;
482;
428;
426;
468;
486;
624;
642;
628;
682;
648;
684;
824;
842;
826;
862;
846;
864.
Sqr(5)sinAcosA=sqr(5)sin2A=1