SOLUTION: Use De moivres theorem to obtain the identity for the following A. Sin(7θ) B. Cos(6θ)

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Question 1144070: Use De moivres theorem to obtain the identity for the following
A. Sin(7θ)
B. Cos(6θ)
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
Using DeMoivre's theorem:



Using the binomial theorem:





Then we use

i2 = -1
i3 = -i
i4 = 1
i5 = i
i6 = -1
i7 = -i



We can equate the two expressions for cos(7q) + i∙sin(7q)



We equate the REAL parts on each side:





We equate the IMAGINARY parts on both sides:



Dividing through by i:



So we have identities for both cos(7q) and sin(7q)

You do the other one the same way.  I'll help you with the binomial theorem part:



Edwin
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