tanα/2=3,求tan(α-π/4)和6sinα-cosα/3sinα+4cosα

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tanα/2=3,求tan(α-π/4)和6sinα-cosα/3sinα+4cosαtanα/2=3,求tan(α-π/4)和6sinα-cosα/3sinα+4cosαtanα/2=3,求tan(

tanα/2=3,求tan(α-π/4)和6sinα-cosα/3sinα+4cosα
tanα/2=3,求tan(α-π/4)和6sinα-cosα/3sinα+4cosα

tanα/2=3,求tan(α-π/4)和6sinα-cosα/3sinα+4cosα
tanα/2=3
tanα
=2tanα/2/(1-tan²α/2)
=2*3/(1-3²)
=6/(-8)
=-3/4
tan(α-π/4)
=(tanα-tanπ/4)/(1+tanαtanπ/4)
=(tanα-1)/(1+tanα)
=(-3/4-1)/(1-3/4)
=(-7/4)/(1/4)
=-7
(6sinα-cosα)/(3sinα+4cosα)分子分母同时除以cosα
=(6sinα/cosα-cosα/cosα)/(3sinα/cosα+4cosα/cosα)
=(6tanα-1)/(3tanα+4)
=(-3/4*6-1)/(-3/4*3-4)
=(-11/2)/(-25/4)
=11/2*4/25
=22/25