设α属于(-π,0),且cos(α+π/6)=4/5,则sin(2α+π/12)的值为
问题描述：
设α属于(-π,0),且cos(α+π/6)=4/5,则sin(2α+π/12)的值为
答
α∈(-π,0)α+π/6∈(-5π/6,π/6)cos(α+π/6)=4/5>0∴α+π/6∈(-π/6,π/6)∴2α+π/3∈(-π/3,π/3)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/3)sin(2α+π/3...