Question

Il proove that
(cos a+Iain a)(cos b+ isin b)=cos(a+b)+I sin (a+b)​

Answer 1

Answer:

Step-by-step explanation:

(CosA + iSinA)(CosB + iSinB)

= CosACosB + iCosASinB + iSinACosB + i²SinASinB

= CosACosB - SinASinB + i(SinACosB + CosASinB)

= Cos(A+B) + iSin(A+B)         (∵   Cos(A+B) = CosACosB - SinASinB)

                                              (∵   Sin(A+B) = SinACosB + CosASinB)