expansion of sin6A?
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Answered by
1
Answer:
1)sin6A=2sin3A×cos3A
2)sin6A=2tan3A÷1+tan²3A
Answered by
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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