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 реши...

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=2 2)tg75+tg15=sin(75+15)/[cos75cos15]=sin90:[1/2*(cos60+cos90)]= =1:(1/2*1/2)=1:1/4=4 3)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√3 5)cos²x=1:(1+tg²x)=1:(1+4/9)=9/13 cosx=3/√13 sinx=√(1-cos²x)=√(1-9/13)=2/√13 sin2x=2*sinxcosx=2*2/√13*3/√13=12/√13 cos2x=cos²x-sin²x=9/13-4/13=5/13 sin(2x+5π/4)=-sin(2x+π/4)=-sin2x*cosπ/4-cos2x*sinπ/4= =-12/13*√2/2-5/13*√2/2=--17√2/26 6)sin²x=1:(1+ctg²x)=1:(1+4/9)=9/13 sinx=3/√13 cosx=2/√13 cos2x=cos²x-sin²x=4/13-9/13=-5/13 sin2x=2sinxcosx=12/√13 cos(2x+7π/4)=cos(2x-π/4)=cos2xcosπ/4+sin2xsinπ/4= =-5/13*√2/2+12/13*√2/2=7√2/13 7)sin2x=1-(sinx-cosx)²=1-p²