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If a(1), a(2), …..,a(n) are in A.P. with...

If `a_(1), a_(2), …..,a_(n)` are in A.P. with common difference `d ne 0,` then the sum of the series sin `d[sec a_(1) sec a_(n-1) sec a_(n)]` is

A

sin d

B

cos d

C

cosec d

D

sin d cos d

Text Solution

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The correct Answer is:
C
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If a_(1),a-(2),a_(3),………….a_(n) are in A.P. with common differecne d, prove that sin [cosec a_(1)coseca_(2)+cosec a_(2)cosec a_(3)+………….+cosec a_(n-1)cosec a_(n)]=cota_(1)-cota_(n) .

Knowledge Check

  • If a_(1), a_(2), …..,a_(n) are in A.P. with common difference d ne 0, then the sum of the series sin d[sec a_(1)sec a_(2) +..... sec a_(n-1) sec a_(n)] is

    A
    `cosec a_(n)-cosec a`
    B
    `cot a_(n)-cot a`
    C
    `sec a_(n)- sec a_(1)`
    D
    `tan a_(n)- tan a_(1)`

  • If a_(1), a_(2),……..a_(n) are in A.P. with common difference d, then the sum of these series sin d ["cosec a"_(1) "cosec a"_(2) + "cosec a"_(2) "cosec a"_(3) + ......+ ....... + "cosec a"_(n-1) - "cosec a"_(n)]

    A
    `sec a_(1) - sec a_(n)`
    B
    `"cosec a"_(1) - "cosec a"_(n)`
    C
    `cot a_(1) - cot a_(n)`
    D
    `tan a_(1) - tan a_(n)`

  • We know that , if a_(1),a_(2),….a_(n) are in A.P and vice versa . If a_(1),a_(2),…a_(n) are in A.P and vice versa . If a_(1),a_(2)….a_(n) are in A.P with common difference d, then for nay (b gt 0) the numbers b^(a_(1)),b^(a_(2)),b^(a_(3)),....,b^(a_(n)) are in G.P with common ratio b^(d) If a_(1),a_(2),.....a_(n) are positive and in G.P with common ratio r , then for any base b(b gt 0), log_(b) a_(1) , log _(b) a_(2) , ..., log_(b) a_(n) are in A.P with common difference log_(b)r If a,b,c,d are in G.P and a^(x) = b^(y) = c^(z) = d^(v) , then x, y , z , v are in

    A
    A.P
    B
    G.P
    C
    H.P
    D
    None of these

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