# tan nA= nC1 tan A-nC3 tan3A + nC5 tan5A …/1- nC2 tan2A+ nC4 tan4A-…

148 Points
13 years ago

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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