what is the value of cos1+cos2+cos3+..........+cos178+cos179+cos180

Asked by ritamkumar | 24th Dec, 2009, 03:29: AM

Expert Answer:

Using the standard result,

cos a + cos (a+d) + cos (a+2d)..... = [cos (a+(n-1)d/2) sin (nd/2)]/sin d/2

= [cos (1+(180-1)1/2) sin (180x1/2)]/sin (1/2) ...................since a = 1, d = 1, n = 180

= cos (90 + 1/2) sin 90/sin (1/2)

= cos (1/2)/sin (1/2) = cot (1/2) = cot 0.5

Regards,

Team,

TopperLearning.

 

Answered by  | 25th Dec, 2009, 03:47: PM

Queries asked on Sunday & after 7pm from Monday to Saturday will be answered after 12pm the next working day.