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tan nA= nC1 tan A-nC3 tan3A + nC5 tan5A …/1- nC2 tan2A+ nC4 tan4A-…
Dear Sonam
we know
cosnA + iSin nA =(cosA +isinA)n
open bracket with the help of binomial
cosnA + iSin nA =(cosA +isinA)n = cosnA + nC1 cosn-1A(isinA) + nC2cosn-2A(isinA)2 +.......
= (cosnA - nC2cosn-2A(sinA)2 +.... ) + i(nC1 cosn-1A(sinA) - nC3 cosn-3A(sinA)3 .......)
compair Real part
Cos nA = (cosnA - nC2cosn-2A(sinA)2 +.... )
=cosnA(1-nC2 tan2A-nC4 tan3A -…)............................1
compair imaginery part
Sin nA = (nC1 cosn-1A(sinA) - nC3 cosn-3A(sinA)3 .......)
=cosnA(nC1 tanA - nC3(tanA)3 ....... ...........) .............2
devide equatin 2 from 1
tan nA = nC1 tan A-nC3 tan3A + nC5 tan5A …/1- nC2 tan2A+ nC4 tan4A-…
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