Question

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`

Answer 1

Correct Answer - 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`