# the average of sin2` ,sin4`,sin6`,.....,sin 180` is  ---------------???

Grade:

## 1 Answers

Aman Bansal
592 Points
11 years ago

Dear Pragya,

2 sin(2) + 178 sin(178) = 180 sin 2
4 sin (4) + 176 sin(176) = 180 sin 4
6 sin (6) + 174 sin (176) = 180 sin 6
..............
..............
..............
90 sin (90) + 90 sin (180 - 90 ) = 180 sin 90

so avg. = [ sin 2 + sin 4 + sin 6 + sin 8 + .......+ sin 90180 ] x 180

Now . sin a + sin(a+d) + sin (a+2d ) + ...... + sin (a+nd ) = sin (na /2 ) sin ( a + {n-1} d/2 )sin (d/2)

Compaaring with the given series , a = 2 , d =2 , n = 2

so avg. = sin 90 sin ( 2 + 89 )sin 1 = cot 1

Best Of luck

Cracking IIT just got more exciting,It s not just all about getting assistance from IITians, alongside Target Achievement and Rewards play an important role. ASKIITIANS has it all for you, wherein you get assistance only from IITians for your preparation and win by answering queries in the discussion forums. Reward points 5 + 15 for all those who upload their pic and download the ASKIITIANS Toolbar, just a simple  to download the toolbar….

So start the brain storming…. become a leader with Elite Expert League ASKIITIANS

Thanks

Aman Bansal

Askiitian Expert