①sin3π/8*cosπ/8+cos3π/8*sinπ/8=sin(3π/8+π/8)=sinπ/2=1
②原式=sin(3π/7)*cos(2π/5)+cos(3π/7)*sin(2π/5) (化为同角)
=sin(3π/7+2π/5) (两角和的正弦公式的逆运用)
=sin(29π/35)=sin(6π/35)(互补两角的正弦相等)
原式=sin[α+(π/4)]cosπ/4-cos[(π/4)+α]sinπ/4
=sin[α+(π/4)-(π/4)]=sinα
①sin3π/8*cosπ/8+cos3π/8*sinπ/8=sin(3π/8+π/8)=sinπ/2=1
②原式=sin(3π/7)*cos(2π/5)+cos(3π/7)*sin(2π/5) (化为同角)
=sin(3π/7+2π/5) (两角和的正弦公式的逆运用)
=sin(29π/35)=sin(6π/35)(互补两角的正弦相等)
原式=sin[α+(π/4)]cosπ/4-cos[(π/4)+α]sinπ/4
=sin[α+(π/4)-(π/4)]=sinα