sin(π-α)-cos(π+α)=√2/3
sinα+cosα=√2/3
(sinα+cosα)^2=2/9
(sinα)^2+2sinαcosα+(cosα)^2=2/9
1+2sinαcosα=2/9
2sinαcosα=-7/9
sinαcosα=-7/18
1-2sinαcosα=16/9
(sinα-cosα)^2=16/9
sinα-cosα=±4/3
sin^3(π/2-α)-cos^3(π/2+α)
=cos^3α+sin^3α
=(cosα+sinα)(sin^2α-sinαcosα+cos^2α)
=√2/3(1-sinαcosα)
=√2/3(1+7/18)
=√2/3*25/18
=25√2/54