∵a∈(0.5π,π)
∴a+π/4∈(3π/4,5π/4)
又∵sin(a+π/4)=1/2
∴a+π/4∈(3π/4,π)
∴a∈(π,3π/4)
∴a+π/4=5π/6
∴a=7π/6
sin2a=sin7π/3=√3/2
cos2a=cos7π/3=1/2