sin(a-b)= sin(a)* cos(b)-cos(a)* sin(b)

cos(a+b)= cos(a)* cos(b)-sin(a)* sin(b)

cos(a-b)= cos(a)* cos(b)+sin(a)* sin(b)

therefore

1，sin 25/ 12πsin 1 1/6π-cos 25/ 12πcos 1 1/6π

=-cos(25/ 12π+ 1 1/6π)

= - cos(47/ 12π)

2，sina= 15/ 17，COSA = √( 1-( 15/ 17)2)= 8/ 17。

cos(a-π/3)

= cos(a)cos(π/3) + sind(a)sin(π/3)

=8/ 17 * 1/2 + 15/ 17 * √3/2

=4/ 17+ 15√3/34