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Home / Doubts and Solutions/JEE/Mathematics

Prove that

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Asked by Anish 11th July 2018, 1:25 PM
Answered by Expert
Answer:
begin mathsize 16px style Using space De space Moivre apostrophe straight s space theorem left parenthesis cosA plus isinA right parenthesis to the power of 5 equals cos 5 straight A plus isin 5 straight A Applying space binomial space theorem space on space LHS space and space solving space it space further space we space get left parenthesis cos to the power of 5 straight A minus 10 cos cubed Asin squared straight A plus 5 cosAsin to the power of 4 straight A right parenthesis plus straight i left parenthesis 5 cos to the power of 4 AsinA minus 10 cos squared Asin cubed straight A plus sin to the power of 5 straight A right parenthesis equals cos 5 straight A plus isin 5 straight A Equating space real space and space imaginary space coefficients space cos 5 straight A equals cos to the power of 5 straight A minus 10 cos cubed Asin squared straight A plus 5 cosAsin to the power of 4 straight A sin 5 straight A equals 5 cos to the power of 4 AsinA minus 10 cos squared Asin cubed straight A plus sin to the power of 5 straight A end style
Answered by Expert 12th July 2018, 11:47 AM
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