已知sin(x+π/12)²-sin(x-π/12)²=1/4,x∈（π/4,π/2),求tanx.
问题描述：
已知sin(x+π/12)²-sin(x-π/12)²=1/4,x∈（π/4,π/2),求tanx.
答
[sin(x+π/12)+sin(x-π/12)][sin(x+π/12)-sin(x-π/12)]=1/4
(sinxcosπ/12+cosxsinπ/12+sinxcosπ/12-cosxsinπ/12)(sinxcosπ/12+cosxsinπ/12-sinxcosπ/12+cosxsinπ/12)=1/4
4sinxcosπ/12*cosxsinπ/12=1/4
(2sinxcosx)(2sinπ/12cosπ/12=1/4
sin2xsinπ/6=1/4
sin2x=1/2
π/4