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

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 Real  part

 Cos nA = (cosⁿA  - ⁿC₂cos^n-2A(sinA)² +.... )

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

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