lg(sinx+cosx)
=1/2(3lg2-lg5)
=1/2(lg8-lg5)
=1/2lg(8/5)
=lg(√(8/5))
∴sinx+cosx=√(8/5)
两边平方
1+2sinxcosx=8/5
2sinxcosx=3/5
∵
(cosx-sinx)²
=1-2sinxcosx
=1-3/5
=2/5
∵0