Question

Упростить:

sin³(2a) cos(6a) + cos³(2a) sin(6a)

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Answer 1

Ответ:Sin³ 2a·Cos³ 2a·Cos 6a·Sin 6a = 1/8 Sin ³4a·1/2·Sin 12a= 1/16Sin³ 4a·Sin 12 a=

=1/16 Sin³4a·(3Sin 4a - 4Sin³4a) = 3/16Sin^4 4a - 1/4 Sin^6 4a

Answer 2

sin³2α=sin2α·sin²2α=sin2α·(1-cos²2α)=sin2α-sin2αcos²2α

cos³2α=cos2α·cos²2α=cos2α·(1-sin²2α)=cos2α-cos2α·sin²2α

sin³2α cos6α + cos³2α sin6α=

=(sin2α-sin2αcos²2α)·cos6α+(cos2α-cos2α·sin²2α)·sin6α=

=sin2α·cos6α-sin2α·cos²2α·cos6α+cos2α·sin6α-cos2α·sin²2α·sin6α=

группируем

=(sin2α·cos6α+cos2α·sin6α)-(sin2α·cos²2α·cos6α+cos2α·sin²2α·sin6α)=

=sin8α-sin2α·cos2α·(cos2α·cos6α+sin2α·sin6α)=

=sin8α-(1/2)sin4α·cos4α=

=sin8α-(1/4)sin8α=(3/4)sin8α

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