Treść zadania

Najlepsze rozwiązanie

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  1 0

  zefir46 15.1.2013 (17:29)

  zad.75
  
  a)
  (1-sin^2&) sin^2&+cos^2&-sin^2& cos^2&
  --------------=-------------------------------------=--------------=ctg&
  sin&*cos& sin&*cos& sin&*cos&
  
  
  
  b)1+cos^2-sin^2&=sin^2&+cos^2&+cos^2&-sin^2&=2cos^2&
  
  c)(sin&+cos&)^2-2sin&cos&=sin^2&+2sin&cos&+cos^2&-2sin&cos&=sin^2&+cos^2&=1
  
  
  zad.76
  
  a)(sin&+cos&)^2+(sin&-cos&)^2=2
  
  L=(sin&+cos&)^2+(sin&-cos&)^2=sin^&+2sin&cos&+cos^2&+sin^2&-2sin&cos&+cos^2&=sin^2&+cos^2&+sin^2&+cos^2&=1+1=2
  L=P
  
  b)
  1-cos^2&=sin^2&
  
  L=1-cos^2&=1-(1-sin^2&)=1-1+sin^2&=sin^2&
  L=P
  
  c)cos^2&-sin^2&=1-2sin^2&
  L=cos^2&-sin^2&=1-sin^2&-sin^2&=1-2sin^2&
  L=P
  
  d)
  1/cos&-cos&=tg&*sin&
  
  L=1/cos&-cos&=(sin^2&+cos^2&)/cos& -cos^2&/cos&=(sin^2&+cos^2&-cos^2&)/cos&=
  
  sin^2&/cos&=sin&*sin&/cos&=tg&*sin&
  
  L=P
  
  e)
  cos^2&*sin&+sin^3&=sin&
  
  L=cos^2&*sin&+sin^3&=sin&(cos^2& + sin^2&)=sin&*1=sin&
  L=P
  
  f)
  (1+sin&)(1/cos&-tg&)=cos&
  
  L=(1+sin&)(1/cos&-tg&)=(1+sin&)(1/cos&-sin&/cos&)=(1+sin&)[(1-sin&)/cos&]=(1-sin2&)/cos&=
  =cos^2&/cos&=cos&
  L=P
  
  g)cos&-cos&sin^2&=cos^3&
  L=cos&-cos&sin^2&=cos&(1-sin^2&)=cos&cos^2&=cos^3&
  L=P
  
  h)
  (sin^3&+sin&cos^2&)/cos^3&+cos&sin^2&=tg&
  
  L=(sin^3&+sin&cos^2&)/(cos^3&+cos&sin^2&)=[sin&(sin^2&+cos^2&)]/[cos&(cos^2&+sin^2&)]=
  =sin&*1/cos&*1=sin&/cos&=tg&
  L=P

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