令a=sinx,b=cosx
则2a^2-ab-b^2=1
a^2+b^2=1
两式相减得：a^2-ab-2b^2=0
(a-2b)(a+b)=0
得：a=2b or a=-b
即：tanx=2 or tanx=-1
得：x=kπ+arctan2 or kπ-π/4