IIT JEE , AIEEE Forum - Mathematics , Algebra - Progressions+ trigno

rohanrony

if a₁, a₂,a₃,.......a_n are in AP with common diff. d , then find sum of the series- sind*[cosec(a₁).cosec(a₂) + cosec(a₂).cosec(a₃) + ........cosec(a_n-1).cosec(a_n)]

1) sec(a₁) - sec (a_n)

2) cosec (a₁₎ - cosec (a_n)

3) cot(a₁) - cot (a_n)

4) tan(a₁) - tan(a_n)

please explain

answer- option 3

abhujabal

sind ( (1/sina1 sina2) + (1/sina2 sina3) + .......)
= sind/ (sina1 sina2) + sind/ (sina2 sina3) + ......
= sin(a2-a1)/(sina1sina2) + ......
= cota1-cota2 + cota2-cota3 + ...... +cotan-1 - cotan
= cota1 - cotan
I hope the answer is correct
Please rate if it helps u......

scadez

consider
sind[cosec(a1)cosec(a2)+...............+cosec(an-1)cosec(an)]
sind[1/sina1sina2+1/sina2sina3+.............+1/sinan-1sinan]
open the brackets.......
sind/sina1sina2+..........sind/sinan-1sinan.
we know that a2-a1=a4-a3=an-an-1=d
hence.......
sin(a2-a1)/sina1sina2+sin(a3-a2)/sina2sina3+...+sin(an-an-1)/sinansinan-1
sina1cosa2-cosa1sina2/sina1sina2+...............+sinan-1cosan-cosan-1sinan/sinansinan-1
cota1-cota2+cota2-cota3+..............+cotan-1-cotan
cota1-cotan

Ask & Discuss Questions with Community & Experts