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Sin nA= cosnA(nC1 tan A-nC3 tan3A +nC5 tan5A-…)
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 imaginery part
Sin nA = (nC1 cosn-1A(sinA) - nC3 cosn-3A(sinA)3 .......)
=cosnA(nC1 tanA - nC3(tanA)3 ....... ...........)
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