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cos nA= cos n A(1- n C 2 tan 2 A- n C 4 tan 3 A -…)


cos nA= cosnA(1-nC2 tan2A-nC4 tan3A -…)


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 Real  part

 Cos nA = (cosnA  - nC2cosn-2A(sinA)2 +.... )

              =cosnA(1-nC2 tan2A-nC4 tan3A -…)

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Badiuddin


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