0identitati_trigonometrice

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Page 1: 0identitati_trigonometrice

Identitati trigonometrice-clasa a-IX-a

Exercitii rezolvate sau cu indicatii.Formule utile:

1) sin(x+y)=sinx cosy+siny cosx ; 2) sin(x-y)=sinx cosy-siny cosx ;2) cos(x+y)=cosx cosy-sinx siny ; 4) cos(x-y)=cosx cosy+sinx siny.4) sin2x=2sinx cosx; 5) cos2x=cos2x-sin2x=2cos2x-1=1-2sin2x .

Aplicatii:1)Aratati ca urmatoarele egalitati sunt adevarate:

a) 1+sinx-cosx=2 ;

Solutiie: sin = = =sinx+1-cosx

=1+sinx-cosx ; sau: 1+sinx-cosx=

= = = = .

b)1+cosx+cos2x=4 cosx cos ;

Solutie:1+cosx+cos2x=2cos2x+cosx=2 cosx =2 cosx =

= 4 cosx ; sau:

= =

=1+cosx+cos2x.

c) 1+sinx+cosx-tgx=

Solutie:

1+sinx+cosx-tgx= = =

d) sinx+siny+sin(x+y)=

Solutie:

Exercitii selectate de prof.Iacovici Emilia

Page 2: 0identitati_trigonometrice

sinx+siny+sin(x+y)=

Exercitii selectate de prof.Iacovici Emilia