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Sin nA= cos n A( n C 1 tan A- n C 3 tan 3 A + n C 5 tan 5 A-…)


Sin nA= cosnA(nC1 tan A-nC3 tan3A +nC5 tan5A-…)


Grade:11

1 Answers

Badiuddin askIITians.ismu Expert
148 Points
12 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 imaginery part

 Sin nA = (nC1 cosn-1A(sinA) - nC3 cosn-3A(sinA)3 .......)

              =cosnA(nC1 tanA - nC3(tanA)3 .......  ...........)

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Badiuddin


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