已知tan(x-π/4）=2 求（sin2x+cos2x）/（2cos²x-3sin2x-1)
问题描述：
已知tan(x-π/4）=2 求（sin2x+cos2x）/（2cos²x-3sin2x-1)
答
tanx
=tan[(x-π/4)+π/4]
=[tan(x-π/4)+tan(π/4)]/[1-tan(x-π/4)tan(π/4)]
=(2+1)/(1-2*1)
=-3
(sin2x+cos2x)/(2cos²x-3sin2x-1)
=(2sinxcosx+cos²x-sin²x)/(2cos²x-6sinxcosx-sin²x-cos²x)
=(2sinxcosx+cos²x-sin²x)/(cos²x-6sinxcosx-sin²x)
分子分母同时除以 cos²x
=(2tanx+1-tan²x)/(1-6tanx-tan²x)
=(-6+1-9)/(1+18-9)
=-14/10
=-7/5