The value of `cot (sum_(n=1)^(23) cot^(-1) (1 + sum_(k=1)^(n) 2k))` isA. `(23)/(25)`B. `(25)/(23)`C. `(23)/(24)`D. `(24)/(23)`

The value of `cot (sum_(n=1)^(23) cot^(-1) (1 + sum_(k=1)^(n) 2k))` is

1.	The value of `cot (sum_(n=1)^(23) cot^(-1) (1 + sum_(k=1)^(n) 2k))` isA. `(23)/(25)`B. `(25)/(23)`C. `(23)/(24)`D. `(24)/(23)`
Answer» Correct Answer - B `cot(underset(n =1)overset(23)sum cot^(-1) (n^(2) + n + 1))` `= cot(underset(n =1)overset(23)sum tan^(-1) ((n + 1 -n)/(1+ n (n + 1))))` `= cot (underset(n=1)overset(23)sum (tan^(-1) (n +1) - tan^(-1)n))` `=cot (tan^(-1) 24 -tan^(-1) 1) rArr cot (tan^(-1) ((23)/(25)))` `= (25)/(23)`

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