根据已知条件,sin(π-a)-cos(π+a)=sqrt(2)/3,
因为sin(π-a)=sin(a),cos(π+a)=-cos(a),
所以上式等价于
sin(a)+cos(a)=sqrt(2)/3,(*)
因为sin^2(a)+cos^2(a)=1,
所以
(sin(a)-cos(a))^2
=2*(sin^2(a)+cos^2(a))-(sin(a)+cos(a))^2
=2*1-(sqrt(2)/3)^2
=2-2/9
=16/9,
并且由于π/2小于a小于π,故sin(a) > 0 > cos(a),
所以sin(a)-cos(a)>0,故
sin(a)-cos(a)=sqrt(16/9)=4/3.