1、Sinx/2 - cosx/2=-√5/2两边平方得,
(sinx/2)^2+(cosx/2)^2-2sinx/2*cosx/2=5/4
而(sinx/2)^2+(cosx/2)^2=1,2sinx/2*cosx/2=sinx
上式变形为1+sinx=5/4,所以sinx=1/4
cos2x=1-2(sinx)^2=1-2*(1/4)^2=1-1/8=7/8
2、函数满足1+tanx>0,即tanx>-1=tan(kπ-π/4)
所以x属于区间(kπ-π/4,kπ+π/2)即为Y=lg(1+tanx)的定义域