已知cos（a＋π/4)=1/3，a为锐角，求cosa、sina的值
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cos（a＋π/4)=1/3
所以
sin（a＋π/4)=2√2/3
cosa=cos(a＋π/4-π/4)
=cos(a＋π/4)cosπ/4+sin(a＋π/4)sinπ/4
=1/3*√2/2+2√2/3*√2/2
=(√2+4)/6
sina=sin(a＋π/4-π/4)
=sin(a＋π/4)cosπ/4-cos(a＋π/4)sinπ/4
=2√2/3*√2/2-1/3*√2/2
=(4-√2)/6
所以
sin（a＋π/4)=2√2/3
cosa=cos(a＋π/4-π/4)
=cos(a＋π/4)cosπ/4+sin(a＋π/4)sinπ/4
=1/3*√2/2+2√2/3*√2/2
=(√2+4)/6
sina=sin(a＋π/4-π/4)
=sin(a＋π/4)cosπ/4-cos(a＋π/4)sinπ/4
=2√2/3*√2/2-1/3*√2/2
=(4-√2)/6
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