已知sin(π/4-a)=5/13(0<a<π/4),求cos(π/4+a)/cos2a

问题描述:

已知sin(π/4-a)=5/13(0<a<π/4),求cos(π/4+a)/cos2a

sin(π/4-a)=5/13=cos(π/4+a)
0sin2a=cos(π/2-2a)=1-2(sin(π/4-a))^2=1-50/169=119/169
cos2a=√(288*50)/169≡120/169
(5/13)/(120/169)=13/24