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  • 1.已知數(shù)列{an}的前四項(xiàng)和等于4,設(shè)前n項(xiàng)和為Sn,且n≥2時(shí),an=1/2(根號(hào)Sn+根號(hào)Sn-1),求S10

    1.已知數(shù)列{an}的前四項(xiàng)和等于4,設(shè)前n項(xiàng)和為Sn,且n≥2時(shí),an=1/2(根號(hào)Sn+根號(hào)Sn-1),求S10
    2.在△ABC中,角A.B.C所對(duì)的邊分別是a.b.c,tanA=1/2,cosB=3倍根號(hào)10/10,
    ①求tanC的值;②若△ABC的最長(zhǎng)邊是1,求最短邊的長(zhǎng).
    數(shù)學(xué)人氣:226 ℃時(shí)間:2020-05-19 00:55:19
    優(yōu)質(zhì)解答
    1.
    a[n] = S[n]-S[n-1] = 1/2 (√S[n]+√S[n-1])
    ==> √S[n] - √S[n-1] = 1/2
    ==> √S[10] - √S[4] = 1/2 * 6 = 3,√S[4]=√4=2
    ==> √S[10] = 5,
    ==> S[10] = 25
    2.
    tanB = sinB/cosB = 1/3
    ==> tan(A+B) = (1/2+1/3)/(1-1/2*1/3) = 1
    ==> tanC = -tan(A+B) = -1
    sinA=√5/5,sinB=√10/10,sinC=√2/2
    ==> sinC>sinA>sinB ==> c>a>b
    ==> b/c = sinB/sinC = √5/5
    ==> b=√5/5
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