0

Guest

Courses New

simplify sinA+sin(A+B)+sin(A+2*B)+........+sin(A+(n-1)*B)

simplify sinA+sin(A+B)+sin(A+2*B)+........+sin(A+(n-1)*B)

Grade:12th pass

1 Answers

Aditya Varshney
20 Points
4 years ago
  1. Multiply and divide each side by 2sin(B/2)
=  {[2sin(B/2)sinA + 2sind(B/2)sin(A+B) + 2sind(B/2)sin(A+2B) ….............+ 2sin(B/2)sin(A+(n-1)B)] }1/ 2sin(B/2)
{2sinXsinY = cos(X-Y) – cos(X+Y}
​=  {[cos(A - (B/2)) – cos(A + (B/2)) + cos (A + (B/2)) – cos (A + (3B/2)) + cos (A + (3B/2) …................... cos(A + (n-3/2)B) – cos (A + (n - 1)/2B)] 1}/2sin (B/2)
= { [cos (A – B/2) – cos(A + (n-1)2B]}1/2sin(B/2)
  1.  multiply and divide by 2
= 1/sin(B/2) 2 sin((2A+(n-1)B)/2)sin(nB/2)
= {sin(nB/2)(sin( (1st angle) + sin(last angle) )/2) }1/sin(B/2)
 
where n = number of terms

Think You Can Provide A Better Answer ?

Other Related Questions on Trigonometry

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More