Question

Demonstrati:
(cosx+cos2x)(2cosx-1)=cos3x+1

Answer 1

Hai sa spargem parantezele poate obtinem ceva:
(cos x+cos2x)(2cosx-1)=cos3x+1
2cos²x-cos x+2*cos2x*cos x-cos 2x=cos3x+1
2cos²x-cosx + 2 * 1/2 (cos3x + cos x) -cos 2x= cos3x +1
2cos²x-cos x+cos3x+cos x-cos2x= cos3x+1
2cos²x-1+cos3x+cos2x=cos3x
-cos2x+cos3x+cos2x=cos 3x
   cos3x=cos 3x Q.E.D
Observatie: Am folosit identitatiile:
cos 2x= 2cos²x - 1
cos a *cos b= 1/2*[cos(a+b)+cos(a-b)]