Math, asked by XxxxDEVILxxxX, 1 year ago

expansion of sin6A?​

Answers

Answered by PrathameshGajare
1

Answer:

1)sin6A=2sin3A×cos3A

2)sin6A=2tan3A÷1+tan²3A

Answered by phoenixadi2907
1

Answer:

sin(6A) = 6cos^5(A)sin(A) - 20cos^3(A)sin^3(A) + 6cos(A)sin^5(A)

Step-by-step explanation:

(cos A + isin A)^n = cos nA + isin nA  

Since you want sin(6A) then all you need to use the binomial coefficients to assist you. For 6 they are 1 6 15 20 15 6 1  

(cos A isin A)^6 = cos^6(A) + i6sin(A)Cos^5(A) + 15i^2sin^2(A)cos^4(A) + i^3*20sin^3(A)cos^3(A) + 15i^4cos^2(A)sin^4(A) + i^5*6cos(A)sin^5(A) + i^6sin^6(A)  

cos^6(A) + i(6cos^5(A)sin(A)) - 15cos^4(A)sin^2(A) - i(20cos^3(A)sin^3(A)) + 15cos^2(A)sin^4(A) + i(6cos(A)sin^5(A)) - 6sin^6(A)  

Note: You want only the terms associated with i. This gives  

sin(6A) = 6cos^5(A)sin(A) - 20cos^3(A)sin^3(A) + 6cos(A)sin^5(A)

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