Home
Class 12
MATHS
If a(1), a(2), a(3), ………., a(n) are in A...

If `a_(1), a_(2), a_(3), ………., a_(n)` are in AP with common difference 5 and if `a_(i)a_(j) ne -1` for i, j = 1, 2, …….., n, then `tan^(-1)((5)/(1+a_(1)a_(2))) + tan^(-1)((5)/(1+a_(2)a_(3))) +……..+ tan^(-1)((5)/(1+a_(n-1)a_(n)))` is equal to a)`tan^(-1)((5)/(1+a(n)a_(n-1)))` b)`tan^(-1)((5)/(1+a(n)a_(n)))`c)`tan^(-1)((5n-5)/(1+a(n)a_(n+1)))` d)`tan^(-1)((5n-5)/(1+a_(1)a_(n)))`

A

`tan^(-1)((5)/(1+a(n)a_(n-1)))`

B

`tan^(-1)((5)/(1+a(n)a_(n)))`

C

`tan^(-1)((5n-5)/(1+a(n)a_(n+1)))`

D

`tan^(-1)((5n-5)/(1+a_(1)a_(n)))`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Similar Questions

Explore conceptually related problems

tan^(-1)""(m)/(n)-tan^(-1)""(m-n)/(m+n) is equal to a) tan^(-1)""(n)/(m) b) tan^(-1)""(m+n)/(m-n) c) (pi)/(4) d) tan^(-1)((1)/(2))

If a_1,a_2,a_3,…….a_n is an AP with common difference d then tan[tan^(-1)(d/(1+a_1a_2))+tan^(-1)((d)/(1+a_2a_3))+...+tan^(-1)((d)/(1+a_(n-1)a_n))] is equal to a) ((n-1)d)/(a_1+a_n) b) ((n-1)d)/(1+a_1a_n) c) (nd)/(1+a_1a_n) d) (a_n-a_1)/(a_n+a_1)

sum_(r=1)^(n) tan^(-1)(2^(r-1)/(1+2^(2r-1))) is equal to a) tan^(-1)(2^n) b) tan^(-1)(2)^n-pi/4 c) tan^(-1)(2^(n+1)) d) tan^(-1)(2^(n+1))-pi/4

If a_1,a_2,…………..a_n are in AP with common difference d ne 0 then find (sin d) [sec a_1 sec a_2+ sec a_2 sec a_3+…….+sec a_(n-1) sec a_n]

If a_(1), a_(2), a_(3),…….,a_(20) are in AP and a_(1) + a_(20) = 45 , then a_(1) + a_(2) + a_(3)+……+a_(20) is equal to

If a_(1) , a_(2), a_(3) , cdots ,a_(n) are in A.P. with a_(1) =3, a_(n) =39 and a_(1) +a_(2) + cdots +a_(n) =210 then the value of n is equal to

If a_(1), a_(2), a_(3),….,a_(n) are in AP and a_(1) = 0 , then the value of ((a_(3))/(a_(2)) + (a_(4))/(a_(3)) +...+(a_(n))/a_(n-1))-a_(2) ((1)/(a_(2)) + (1)/(a_(3))+...+(1)/(a_(n-2))) is equal to a) (n-2) + (1)/((n-2)) b) (1)/((n-2)) c)(n - 2) d)(n - 1)

If a_(1), a_(2),a_(3), cdots , a_(2n+1) are in A.P then (a_(2n+1)-a_(1))/(a_(2n+1)+a_(1)) + (a_(2n)-a_(2))/(a_(2n)+a_(2))+cdots+ (a_(n+_2)-a_(n))/(a_(n+2)+a_(n)) is equal to

If a_(1), a_(2), a_(3), a_(4) are in AP, then (1)/(sqrt(a_(1)) + sqrt(a_(2))) + (1)/(sqrt(a_(2)) + sqrt(a_(3))) + (1)/(sqrt(a_(3)) + sqrt(a_(4))) is equal to

If a_(1), a_(2), …, a_(50) are in GP, then " "(a_(1)-a_(3)+a_(5)-…+a_(49))/(a_(2)-a_(4)+a_(6)-…+a_(50)) is equal to :