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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 Question
for 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??????
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)
Heartful Thanks......!!!!!
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