Question

cos a+cos(a+b)+cos(a+2b)+.......+cos(a+nb)=??​

Answer 1

Answer:

don't know sorry be my friend

Answer 2

Answer:

Let

C=Cos(A)+Cos(A+B)+⋯+Cos(A+(n−1)B)

and

S=Sin(A)+Sin(A+B)+⋯+Sin(A+(n−1)B)

if

i=−1−−−√

Consider

C+iS=eiA+ei(A+B)+⋯+ei(A+(n−1)B)

⟹

C+iS=eiA(1+eiB+ei2B+⋯+ei(n−1)B)

⟹

C+iS=eiA(einB−1eiB−1)

⟹

C+iS=ei(A+(n−1)B2)Sin(nB2)Sin(B2)

From this we get Real and Imaginary parts as the Required Results.

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