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Asked by Varsneya Srinivas 21st February 2018, 10:48 AM
Answered by Expert
Answer:
begin mathsize 16px style straight x squared minus 2 straight x space cosα plus 1 equals open parentheses straight x minus straight e to the power of iα close parentheses open parentheses straight x minus straight e to the power of negative iα end exponent close parentheses.... euler apostrophe straight s space form space space space space space straight e to the power of iα equals cosα plus isinα
So comma space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space straight e to the power of negative iα end exponent equals cosα minus isinα
straight x equals straight e to the power of plus-or-minus iα end exponent
similarly
straight y equals straight e to the power of plus-or-minus iβ end exponent
2 cos left parenthesis straight alpha plus straight beta right parenthesis equals straight e to the power of straight i left parenthesis straight alpha plus straight beta right parenthesis end exponent plus straight e to the power of negative straight i left parenthesis straight alpha plus straight beta right parenthesis end exponent
equals straight e to the power of straight i left parenthesis straight alpha right parenthesis end exponent straight e to the power of straight i left parenthesis straight beta right parenthesis end exponent plus fraction numerator 1 over denominator straight e to the power of straight i left parenthesis straight alpha right parenthesis end exponent straight e to the power of straight i left parenthesis straight beta right parenthesis end exponent end fraction
equals xy plus 1 over xy
also
straight x over straight y plus straight y over straight x
end style
Answered by Expert 21st February 2018, 5:50 PM
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