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 Exercise [05.08] 
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Joined: 12 Mar 2008, 10:57
Posts: 69
Location: India
Post Exercise [05.08]
e^{i3\theta}=(e^{i\theta})^3
\Rightarrow\ \cos{3\theta}+i\sin{3\theta}
=(\cos{\theta}+i\sin{\theta})^3
=\cos^{3}{\theta}-i\sin^{3}{\theta}+i3\cos^{2}{\theta}\sin{\theta}-3\cos{\theta}\sin^{2}{\theta}
=\cos^{3}{\theta}-3\cos{\theta}\sin^{2}{\theta}+i(3\cos^{2}{\theta}\sin{\theta}-\sin^{3}{\theta})
Equating real and imaginary parts we get
\cos{3\theta}=\cos^{3}{\theta}-3\cos{\theta}\sin^{2}{\theta}and
\sin{3\theta}=3\cos^{2}{\theta}\sin{\theta}-\sin^{3}{\theta}


23 May 2008, 09:55
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