You can put this solution on YOUR website! .
using de'Moivres formula evaluate sin(5theta)/sin(theta) and leave your answer in cos(theta)
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This problem is for those students who know complex numbers and Trigonometry very well and want to rise their level from good to perfect.
I will show you how to solve it for more simple (but still very close) formulation:
Using de'Moivres formula evaluate and leave your answer in terms of cos(a).
Solution
Consider complex number z = cos(a) + i*sin(a).
According to de'Moivre formula,
= = . (1)
By applying Newton's binomial formula to and accounting that = -1, you get
= = . (2)
From (1) and (2), you get for the imaginary part coefficients
sin(3a) = - . (3)
Next step divide both sides of (3) by sin(a). You will get
= . (4)
Your last step is to replace in the RHS of (4) by :
= = .
Answer. Using de'Moivre formula, we get = .
Doing by the same way, you can solve the problem for .
