化简 sin17/8*π*cos7/4*π-cos7/8*π*sin3/4*π

化简 sin17/8*π*cos7/4*π-cos7/8*π*sin3/4*π
化简 sin17/8*π*cos7/4*π-cos7/8*π*sin3/4*π

化简 sin17/8*π*cos7/4*π-cos7/8*π*sin3/4*π
sin17π/8*cos7π/4-cos7π/8*sin3π/4
=sin(2π+π/8)*cos(2π-π/4)-cos(π-π/8)*sin(π-π/4)
=sinπ/8*cosπ/4-(-cosπ/8)*sinπ/4
=sinπ/8*cosπ/4+cosπ/8*sinπ/4
=sin(π/8+π/4)
=sin(3π/4)
=sin(π-π/4)
=sinπ/4
=√2/2

sin17/8*π*cos7/4*π-cos7/8*π*sin3/4*π
= sin1/8*π*cos7/4*π-cos7/8*π*sin3/4*π
= sin7/8*π*(-cos3/4*π)-cos7/8*π*sin3/4*π
=-[sin7/8*π*cos3/4*π+cos7/8*π*sin3/4*π]
=-sin(7/8*π*+3/4*π)
=-sin(15/8 π）
=sin(1/8π）