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Question Number 216202 by mahdipoor last updated on 29/Jan/25
prove :   sin(a+b)=sin(a)cos(b)+sin(b)cos(a)
prove:sin(a+b)=sin(a)cos(b)+sin(b)cos(a)
Answered by dionigi last updated on 30/Jan/25
e^(i (a+b) ) = cos(a+b) + i sin(a+b)  e^(i (a+b) ) = e^(ia)  e^(ib)    e^(i (a+b) ) = (cos a + i sin a) (cos b + i sin b)  e^(i (a+b) ) = cos a cos b − sin a sin b                      + i sin a cos b + i cos a sin b  spliting real and imaginary parts  of first and last line  cos(a+b) = cos a cos b −sin a sin b  sin(a+b) = sin a cos b + cos a sin b
ei(a+b)=cos(a+b)+isin(a+b)ei(a+b)=eiaeibei(a+b)=(cosa+isina)(cosb+isinb)ei(a+b)=cosacosbsinasinb+isinacosb+icosasinbsplitingrealandimaginarypartsoffirstandlastlinecos(a+b)=cosacosbsinasinbsin(a+b)=sinacosb+cosasinb
Answered by mehdee7396 last updated on 30/Jan/25
EC=EF×Cosα  &   EB=AE×Sinα  Sin(α+β)=((AD)/(AF))=((EC)/(AF))+((BE)/(AF))  =((EF)/(AF))×Cosα+((AE)/(AF))×Sinα  =SinβCosα+SinαCosβ
EC=EF×Cosα&EB=AE×SinαSin(α+β)=ADAF=ECAF+BEAF=EFAF×Cosα+AEAF×Sinα=SinβCosα+SinαCosβ
Commented by mehdee7396 last updated on 30/Jan/25
Answered by a.lgnaoui last updated on 30/Jan/25
Soit  OB:Cos(a+b)i,(Sin(a+b)j  Calcul de OB/Repere(O,A,A′)  ci−joint demonstration :
SoitOB:Cos(a+b)i,(Sin(a+b)jCalculdeOB/Repere(O,A,A)cijointdemonstration:
Answered by a.lgnaoui last updated on 30/Jan/25

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