设α为锐角,若cos（α+π/6）=4/5,则sin（2α+π/6）=

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由cos（α+π/6）=4/5 推导出→sin（α+π/6）=3/5引入一个sin（2α+π/3）=sin2（α+π/6）=2sin(α+π/6)cos(α+π/6)=2×3/5×4/5=24/25 推导出→cos （2α+π/3）=7/25sin（2α+π/6）=sin[（2α+π/3）-π/6]=s...
======以下答案可供参考======
供参考答案1:
α∈(0,π/2)
α+π/6∈(π/6,2π/3)
cos(α+π/6)=4/5>0∴α+π/6∈(π/6,π/2)
∴2α+π/3∈(π/3,π)
cos(2α+π/3)
=2cos²(α+π/6)-1
=2*(4/5)²-1
=32/25-1
=7/25>0∴2α+π/3∈(π/3,π/2)
sin(2α+π/3)=24/25
sin(2α+π/12)
=sin(2α+π/3-π/4)
=sin(2α+π/3)cosπ/4-cos(2α+π/3)sinπ/4
=24/25*√2/2-7/25*√2/2
=24√2/50-7√2/50
=17√2/50