1) sin^2 П\8+ cos^2 3П\8+sin^2 5П\8+ cos^2 7П\8
2) tg 435+tg375
3) tg 225-tg 195
4) Ctg (13П/12)-ctg(5П/12)
5) sin (2x+5П\4) при tg x=2\3
6) cos (2x+7П\4) при ctg x=2\3
7) sin2x при sinx-cosx=p
Баллов не жалко,но вот решите пожалуйстаа

1)(1-сosπ/4)/2+(1+cos3π/4)/2+(1-cos5π/4)/2+(1+cos7π/4)=1/2*(1-√2/2+1-√2/2+1+√2/2+1+√2/2)=1/2*4=22)tg75+tg15=sin(75+15)/[cos75cos15]=sin90:[1/2*(cos60+cos90)]==1:(1/2*1/2)=1:1/4=43)tg45-tg15=sin(45-15):[1/2*(cos30+cos60)]=1/2:(1/4*(√3+1)=2(√3+1)4)ctgπ/12-ctg5π/12=sin(π/12-5π/12):[1/2*(cosπ/3-cosπ/2)]==-√3/2:[1/2*1/2)=-√3/2*4=-2√35)cos²x=1:(1+tg²x)=1:(1+4/9)=9/13cosx=3/√13sinx=√(1-cos²x)=√(1-9/13)=2/√13sin2x=2*sinxcosx=2*2/√13*3/√13=12/√13cos2x=cos²x-sin²x=9/13-4/13=5/13sin(2x+5π/4)=-sin(2x+π/4)=-sin2x*cosπ/4-cos2x*sinπ/4==-12/13*√2/2-5/13*√2/2=--17√2/266)sin²x=1:(1+ctg²x)=1:(1+4/9)=9/13sinx=3/√13cosx=2/√13cos2x=cos²x-sin²x=4/13-9/13=-5/13sin2x=2sinxcosx=12/√13cos(2x+7π/4)=cos(2x-π/4)=cos2xcosπ/4+sin2xsinπ/4==-5/13*√2/2+12/13*√2/2=7√2/137)sin2x=1-(sinx-cosx)²=1-p²