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# I hav come to encounter an mcq question in an Entrance Material, I tried and got d result but it seems to be wrong when i luk the answer key and the explanation is missing, where as every questions hav solution wid explanantion ...Please help me to solve the given Questionfor convenience. I represent alpha as &Question: If (Cos& + iSin&) (Cos2& + iSin2& ) ( Cos3& + iSin 3&) .......(Cos n& + iSin n& ) = 1. Then & = ________.I got the answer 2(pi)k/n+1, where k = (0,1,2...n).  But in answer key it is 4(pi)m/n(n+1). I dont knw hw does it come and what they mean by m??????

9 years ago

you know that

(isinA+cosA)(isinB+cosB)=(isin(2k∏+A+B)+cos(2k∏+A+B))

hence in the above multiply you will get

cos(&+2&+3&+...n&)+isin(&+2&+3&+...n&)=1   [means imaginary part is 0 and real part is 1]

for cosR=1 => R=2m∏

=>&+2&+3&+...n&=2m∏   [for m=1,2,3]

=>&(1+2+3+...n)=2m∏

= &(n(n+1)/2)=2m∏

hence= &=4m∏/n(n+1)