lg(sinx+cosx)=1/2(3lg2-lg5)=1/2(lg8-lg5)=1/2lg(8/5)=lg(√(8/5))
sinx+cosx=√(8/5)
1+2sinxcosx=8/5
2sinxcosx=3/5
(cosx-sinx)^2=1-2sinxcosx=1-3/5=2/5
∵0sinx
cosx-sinx=√(2/5)=√10/5