Question

已知cos（π-2a）/sin（a-π/4）=根号2/2，求sina+cosa

Answer 1

解：由cos（π-2a）/sin（a-π/4）=√2/2
=-cos(2a)/{(√2/2)[sina-cosa]}=√2/2
得：
cos(2a)/[sina-cosa]
=[cos^2(a)-sin^2(a)]/[sina-cosa]
=[sina+cosa]*[sina-cosa]/[sina-cosa]
=sina+cosa
=-1/2