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

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