Question

Упростите выражение:

Answer 1

Из формул
sin3a=3cos²asina-sin³a    и cos3a=cos³a-3cosasin²a⇒
sin³2a=3cos²2asin2a-sin6a  и  cos³2a=3cos2asin²2a+cos6a

sin³2acos6a+cos³2asin6a=(3cos²2asin2a-sin6a)cos6a+(3cos2asin²2a+cos6a)sin6a=
=3cos²2asin2acos6a-sin6acos6a+3cos2asin²2asin6a+cos6asin6a=
=3cos²2asin2acos6a+3cos2asin²2asin6a=3cos2asin2a(cos2acos6a+sin2asin6a)=
=3cos2asin2acos(6a-2a)=3cos2asin2acos4a=3*1/2sin4acos4a=3/2*1/2sin8a=3/4sin8a