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Evaluate the following using binomial theorem
(CosA + iSinA)^n=

Khushi , 6 Years ago
Grade 11
anser 1 Answers
Aditya Gupta
(CosA + iSinA)^n=(e^iA)^n= e^inA= Cos(nA) + iSin(nA)
note that using binomial theorem we shall get terms of the form nCr cos^(n-r)A(isinA)^r, and equating it to cosnA+isinnA allows us to derive the formula for cosnA and sinnA in terms of cosA and sinA. 
hence, (CosA + iSinA)^n= cosnA+isinnA CANNOT be derived from binomial theorem alone. however, it can be proved using induction also (in case you dont prefer using the eulers formula).
kindly approve :)
Last Activity: 6 Years ago
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