Normal 0 false false false MicrosoftInternetExplorer4 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 ....... ...........) Please feel free to post as many doubts on our discussion forum as you can. If you find any question Difficult to understand - post it here and we will get you the answer and detailed solution very quickly. We are all IITians and here to help you in your IIT JEE preparation. All the best. Regards, Askiitians Experts Badiuddin

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Grade 11Trigonometry

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

Sonam Ghatode

16 Years agoGrade 11

1 Answer

Badiuddin askIITians.ismu Expert

16 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 cos^n-1A(isinA) + ⁿC₂cos^n-2A(isinA)² +.......

= (cosⁿA - ⁿC₂cos^n-2A(sinA)² +.... ) + i(ⁿC₁ cos^n-1A(sinA) - ⁿC₃ cos^n-3A(sinA)³.......)

compair imaginery part

Sin nA = (ⁿC₁ cos^n-1A(sinA) - ⁿC₃ cos^n-3A(sinA)³.......)

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

Please feel free to post as many doubts on our discussion forum as you can.
If you find any question Difficult to understand - post it here and we will get you
the answer and detailed solution very quickly.

We are all IITians and here to help you in your IIT JEE preparation.

All the best.

Regards,
Askiitians Experts
Badiuddin