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If a(1),a(2),a(3),……a(87),a(88),a(89) ar...

If `a_(1),a_(2),a_(3),……a_(87),a_(88),a_(89)` are the arithmetic means between `1` and `89`, then `sum_(r=1)^(89)log(tan(a_(r ))^(@))` is equal to

A

`0`

B

`1`

C

`log_(2)3`

D

`log5`

Text Solution

Verified by Experts

The correct Answer is:
A
`(a)` As `1, a_(1),a_(2),a_(3),……….,a_(87),a_(88),a_(89),89` are in `A.P`.
So, `a_(1)+a_(89)=a_(2)+a_(88)=……..=1+89=90`
`:.sum_(r=1)^(89)log(tana_(r )^(@))`
`=log(tana_(1)^(@)*tana_(2)^(@)……..tana_(88)^(@)*tana_(89)^(@))`
`=log1=0`
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