求 sin19∘cos79∘−sin71∘cos11∘ =?

Sol
Sin19度Cos79度－Sin71度Cos11度
= Sin19度Cos79度－Cos19度Sin79度
=Sin(19度－79度)
=Sin(－60度)
=－√3/2

-0.866025403

sin19∘cos79∘=
1/2(sin(19+79)+sin(19-79))=1/2(sin(98)+sin(-60))=1/2(cos(8)-sin(60))
sin71∘cos11∘ =
1/2(sin(71+11)+sin(79-11))=1/2(sin(82)+sin(60))=1/2(cos(8)+sin(60))

sin19∘cos79∘−sin71∘cos11∘ = 1/2(cos(8)-sin(60))- 1/2(cos(8)+sin(60)) =
-sin(60)=(3^1/2)/2=-0.866