If a1, a2, an are in A.P. with common d...

If `a_1, a_2, a_n` are in A.P. with common difference `d!=0` , then the sum of the series `sind[seca_1seca_2+seca_2seca_3+....+s e ca_(n-1)seca_n]` is : a.`cos e ca_n-cos e ca` b. `cota_n-cota` c. `s e ca_n-s e ca` d. `t a na_n-t a na`

Text Solution

AI Generated Solution

Topper's Solved these Questions

RELATIONS AND FUNCTIONS
CENGAGE ENGLISH|Exercise All Questions|9 Videos
STRAIGHT LINES
CENGAGE ENGLISH|Exercise All Questions|491 Videos

Similar Questions

Explore conceptually related problems

If a_1,a_2,a_3, ,a_n are in A.P. with common difference d(w h e r ed!=0) , then the sum of series. sind (coseca_1 coseca_2+coseca_2 coseca_3 +....+ coseca_(n-1) cos e ca_n) is equal to cot a_1-cot a_n

If a_1,a_2,a_3,--- ,a_n are in A.P with common difference d (where d!=0 ) , then the sum of series. sind(cos e ca_1cos e ca_2+cos e ca_2cos e ca_3+ --+cos e ca_(n-1)cos e ca_n) is equal to cota_1-cota_n

let a_1,a_2,...a_n be in A.P. wth common difference pi/6 . if seca_1seca_2+seca_2seca_3+....seca_(n-1)seca_n = k(tana_n-tana_1) Find the value of k

If theta_1,theta_2,theta_3, ,theta_n are in AP, whose common difference is d , show that sectheta_1s e ctheta_2+s e ctheta_2sectheta_3+....+sectheta_(n-1)sectheta_n=(t a ntheta_n-t a ntheta_1)/(sind)

If theta_1,theta_2,theta_3, ,theta_n are in AP, whose common difference is d , show that sectheta_1s e ctheta_2+s e ctheta_2sectheta_3++sectheta_(n-1)sectheta_n=(tantheta_n-tantheta_1)/(sind)

If a_1,a_2,a_3,…………..a_n are in A.P. whose common difference is d, show tht sum_2^ntan^-1 d/(1+a_(n-1)a_n)= tan^-1 ((a_n-a_1)/(1+a_na_1))

If a_1,a_2,a_3,…….a_n are in Arithmetic Progression, whose common difference is an integer such that a_1=1,a_n=300 and n in[15,50] then (S_(n-4),a_(n-4)) is

Prove: (secA-cos e c\ A)(1+tanA+cotA)=tanAsecA-cotA cos e c\ A .

Prove that s e cA(1-sinA)(s e cA+t a nA)=1

If S_n denotes the sum of n terms of an A.P. whose common difference is d and first term is a, find S_n-2S_(n-1)+S_(n-2)

CENGAGE ENGLISH-SEQUENCES AND SERIES-All Questions

Find the sum 1+2(1+1/50)+3(1+1/50)^(2)+…50 terms.
Text Solution
|
The sum of 50 terms of the series 3/(1^2)+5/(1^2+2^2)+7/(1^2+2^2+3^2)+...
Text Solution
|
If a1, a2, an are in A.P. with common difference d!=0 , then the sum ...
Text Solution
|
The sum of the series a-(a+d)+(a+2d)-(a+3d)+... up to (2n+1) terms is:...
Text Solution
|
If a ,b , a n dc are in G.P. and x ,y , respectively, are the arithmet...
Text Solution
|
If a ,ba n dc are in A.P., and pa n dp ' are respectively, A.M. and ...
Text Solution
|
Find the sum 3/(1xx2)xx1/2+4/(2xx3)xx(1/2)^2+5/(3xx4)xx(1/2)^2+ ton te...
Text Solution
|
If the sum of n terms of the series (2n+1)/(2n-1)+3((2n+1)/(2n-1))^...
Text Solution
|
Let x=1+3a+6a^2+10 a^3+ ,|a|<1. y=1+4b+10 b^2+20 b^3+ ,|b|<1. Find S...
Text Solution
|
If the first and the nth terms of a G.P are a and b , respectively, an...
Text Solution
|
Along a road lie an odd number of stones placed at intervals of 10 met...
Text Solution
|
Find a three – digit number such that its digits are in increasing G.P...
Text Solution
|
If the terms of the A.P, sqrt(a-x),sqrt(x),sqrt(a+x) are all in integ...
Text Solution
|
For a ,x ,>0 prove tht at most one term of the G.P. sqrt(a-x),sqrt(x),...
Text Solution
|
If 1/(1^2)+1/(2^2)+1/(3^2)+ .......=(pi^2)/6,t h e n1/(1^2)+1/(3^2)+1/...
Text Solution
|
Coefficient of x^(18) in (1+x+2x^2+3x^3++18 x^(18))^2 equal to 995 b. ...
Text Solution
|
Let alphaa n dbeta be the roots of x^2-x+p=0a n dgammaa n ddelta be th...
Text Solution
|
If the sum of the first 2n terms of the A.P. 2, 5, 8, ..., is equal to...
Text Solution
|
Statement 1: If the arithmetic mean of two numbers is 5/2 geometric ...
Text Solution
|
Let the positive numbers a ,b ,ca d nd be in the A.P. Then a b c ,a b ...
Text Solution
|