1.已知a×sinA+c×sinC-√2a×sinC=b×sinB①求角B②若A=5π/12,b=2,求边a,边c 2.已知tan (α-β)=1/2,tan β=-1/7,α,β∈(0,π)求2α-β的值
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![1.已知a×sinA+c×sinC-√2a×sinC=b×sinB①求角B②若A=5π/12,b=2,求边a,边c 2.已知tan (α-β)=1/2,tan β=-1/7,α,β∈(0,π)求2α-β的值](/uploads/image/z/683645-5-5.jpg?t=1.%E5%B7%B2%E7%9F%A5a%C3%97sinA%2Bc%C3%97sinC%EF%BC%8D%E2%88%9A2a%C3%97sinC%EF%BC%9Db%C3%97sinB%E2%91%A0%E6%B1%82%E8%A7%92B%E2%91%A1%E8%8B%A5A%EF%BC%9D5%CF%80%2F12%2Cb%EF%BC%9D2%2C%E6%B1%82%E8%BE%B9a%2C%E8%BE%B9c+2.%E5%B7%B2%E7%9F%A5tan+%EF%BC%88%CE%B1%EF%BC%8D%CE%B2%EF%BC%89%EF%BC%9D1%2F2%2Ctan+%CE%B2%EF%BC%9D%EF%BC%8D1%2F7%2C%CE%B1%2C%CE%B2%E2%88%88%EF%BC%880%2C%CF%80%EF%BC%89%E6%B1%822%CE%B1%EF%BC%8D%CE%B2%E7%9A%84%E5%80%BC)
1.已知a×sinA+c×sinC-√2a×sinC=b×sinB①求角B②若A=5π/12,b=2,求边a,边c 2.已知tan (α-β)=1/2,tan β=-1/7,α,β∈(0,π)求2α-β的值
1.已知a×sinA+c×sinC-√2a×sinC=b×sinB①求角B②若A=5π/12,b=2,求边a,边c 2.已知tan (α-β)=1/2,tan β=-1/7,α,β∈(0,π)求2α-β的值
1.已知a×sinA+c×sinC-√2a×sinC=b×sinB①求角B②若A=5π/12,b=2,求边a,边c 2.已知tan (α-β)=1/2,tan β=-1/7,α,β∈(0,π)求2α-β的值
1.1)a×sinA+c×sinC-√2a×sinC=b×sinB 2)sin(5π/6)=2sin(5π/12)cos(5π/12)
a^2+c^2-√2a×c=b^2 =sin(π/6)=1/2
a^2+c^2-b^2=√2a×c sinAcosA=1/4
(a^2+c^2-b^2)/2ac=√2/2=cosB sinA^2+cosA^2=1
sinA=(√6+√2)/4
即cosB=45° a/sinA=b/sinB
已知sinA,sinB,b.易求a、c
2.tan (α-β)=(tanα-tanβ)/1+tanαtanβ=1/2
带入tanβ 得tanα=1/3
∴α∈(0,π/2) ∵tan2α=2tanα/1-tanα^2=3/4 ∴2α∈(0,π/2)
β∈(π/2,π)
tan2α=3/4 tanβ=-1/7
tan(2α-β)=tan2α-tanβ/1+tan2αtanβ=(自己算吧)