If zcos θi sin θ, show thatz" +--2 cos 3θ and z[April 2006, April 2 – InterviewSolution

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1.	If zcos θi sin θ, show thatz" +--2 cos 3θ and z[April 2006, April 2008 (AEI/BM/...), Oct. 2009
Answer» Using De Moviers theoremz^n=(cosA+isinA)^n=cosnA+isinnA1/z=cosA-isinAhence1/z^n=(cosnA-isinnA)..using Demovier theoremHencez^3+1/z^3=cos3A+isin3A+cos3A-isin3A=2cos3Asimilarlyz^3-1/z^3=cos3A+isin3A-cos3A+isin3A=2isin3A

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