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de moivre's theorem


Mangur Muhammad

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hi guys

Please help 

who can solve it for me  ?

 

Below are my solutions. I didn't solve the first 2 problems using De Moivre's theorem, simply because I think it's way easier to solve them with mathematical induction. I have also used lots and lots of trigonometric identities, which I've made implicit in my worked solutions. All of these identities, which I listed below, are part of the IB syllabus, and any HL student should be comfortable using them:

 

gif.latex? \cos{\theta} =2 \cos^2{\frac{

 

gif.latex? \sin{\theta} =2 \sin{\frac{\t

 

gif.latex? \cos{A \pm B} =\cos{A}\cos{B}

 

gif.latex? \sin{A \pm B} =\sin{A}\cos{B}

 

gif.latex? \cos{(-\theta)} =\cos{\theta}

 

gif.latex? \sin{(-\theta)} =-\sin{\theta

 

Feel free to ask if you have any further questions.

 

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