Tg*ctg=1
подставляем:
(-3/5)*(-5/8)=1
3/8=1
неверно, значит не могут
2
sin²68+cos²38+2sin68*cos38+sin²38+cos²68-2sin38*cos68=
=(sin²68+cos²68)+(sin²38+cos²38+2(sin68*cos38-cos68*sin38)=
=1+1*2sin(68-38)=2+2*sin30=2+2*1/2=2+1=3
3
sina=-√(1-cos²a)=-√(1-25/169)=-√(144/169)=-12/13
sin2a=2sina*cosa=2*(-5/13)*(-12/13)=120/169
cos2a=cos²a-sin²a=25/169-144/169=-119/169
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Х^2+4ху-5у^2=(х^2+2*х^2*2у+4у^2)-9у^2=(х+2у)^2-(3у)^2=(х+2у-3у)(х+2у+3у) =(х-у) (х+5у)
Б)
cos²α-(cos(π-α)*sin(π/2-α))/(ctg(π+α)*tg(3π/2-α))= ОДЗ: α≠πn/2, n∈Z.
=cos²α-(-cosα*cosα)/(ctgα*ctgα)=cos²α-(-cos²α/(cos²α/sin²α))=cos²α+sin²α=1.