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Working with De Moivre's theorem

If tan(A) = 1/2, find the value of tan(5A)

Hint: Use De Moivre's theorem.

Solution Preview

Using De Moivre's theorem we can write,

Cos(5A)+i Sin(5A) = {Cos(A)+i Sin(A)}^5

Now expand the right hand side of this equation,

= Cos^5(A)-i 5Cos^4(A) Sin(A)-10Cos^3(A) Sin^2(A)-10 i Cos^2(A) ...

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