Home
Class 12
MATHS
The value of cotsum(n=1)^(19)cot^(-1)(1+...

The value of `cotsum_(n=1)^(19)cot^(-1)(1+sum_(p=1)^(n)2p)` is equal to (a) `(21)/(19)` (b) `(19)/(21)` (c) `-(19)/(21)` (d) `-(21)/(19)`

A

`(23)/(22)`

B

`(19)/(21)`

C

`(22)/(23)`

D

`(21)/(19)`

Text Solution

Verified by Experts

The correct Answer is:
D
`cot (sum_(n=1)^(19)cot^(-1)(1+sum_(p=1)^(n)2p))`
`sum_(P=1)^(n)2P=2+4+6+.......+2n=n^(2)+n`
`sum_(n=1)^(19)cot^(-1)(n^(2)+n+1)`
`sum_(n=1)^(19)tan^(-1)(((n+1)-(n))/(1+n(n+1)))`
`sum_(n=1)^(19)tan^(-1)(n+1)-tan^(-1)n=tan^(-1)20-(pi)/(4)`
`therefore cot(tan^(-1)20-(pi)/(4))=(1)/(tan(tan^(-1)20-(pi)/(4)))=(1+20)/(20-1)=(21)/(19)`
Promotional Banner

Similar Questions

Explore conceptually related problems

The value of cot sum_(n=1)^(19)(cot^(-1)(1+sum_(p=1)^(n)2p)) is equal to ( a )(21)/(19) (b) (19)/(21)(c)-(19)/(21) (d) -(21)/(19)

19^(n) - 1 is

sqrt((0.361)/(0.00169))=?(1.9)/(13) (b) (19)/(13)(c)(1.9)/(130) (d) (190)/(13)

Which of the following fractions is the smallest? (13)/(16) (b) (15)/(19) (c) (17)/(21) (d) (7)/(8)

(14)/(19)xx(57)/(70)xx(20)/(21)=?

What is the value of the following expression? (1)/((2^(2)-1))+(1)/((4^(2)-1))+(1)/((6^(2)-1))+backslash+(1)/((20^(2)-1))(9)/(19) (b) (10)/(19)(c)(10)/(21) (d) (11)/(21)

Evaluate :(6)/(7)-2+(-7)/(9)+(19)/(21)

The value of cos((pi)/(19))+cos((3 pi)/(19))+cos((5 pi)/(19))++cos((17 pi)/(19)) is (a) (1)/(2)(b)0(c)1 (d)none