e v a l u a t e space t h e space f o l l o w i n g colon sin squared 5 plus sin squared 10 plus sin squared 15.......... plus sin squared 80 plus sin squared 85 plus sin squared 90
                  ans - 19/2
 

Asked by reetatyagi8 | 27th Jun, 2015, 06:19: PM

Expert Answer:

C o n s i d e r space t h e space g i v e n space e x p r e s s i o n colon sin squared 5 degree plus sin squared 10 degree plus sin squared 15 degree plus... plus sin squared 80 degree plus sin squared 85 degree plus sin squared 90 degree L e t space u s space r e w r i t e space t h e space a b o v e space e x p r e s s i o n space a s comma sin squared 5 degree plus sin squared 85 degree plus sin squared 10 degree plus sin squared 80 degree plus sin squared 15 degree plus sin squared 75 degree plus sin squared 20 degree plus sin squared 70 degree plus sin squared 25 degree plus sin squared 65 degree plus sin squared 30 degree plus sin squared 60 degree plus sin squared 35 degree plus sin squared 55 degree plus sin squared 40 degree plus sin squared 50 degree plus sin squared 45 degree plus sin squared 90 degree C o n s i d e r space t h e space t e r m s comma sin squared 5 degree plus sin squared 85 degree equals sin squared 5 degree plus sin squared open parentheses 90 degree minus 5 degree close parentheses space space space space space space space space space space space space space space space space space space space space space space space space equals sin squared 5 degree plus cos squared 5 degree space space space space space space space space space space space space space space space space space space space space space space space space equals 1 S i m i l a r l y comma sin squared 10 degree plus sin squared 80 degree equals sin squared 10 degree plus sin squared open parentheses 90 degree minus 10 degree close parentheses space space space space space space space space space space space space space space space space space space space space space space space space equals sin squared 10 degree plus cos squared 10 degree space space space space space space space space space space space space space space space space space space space space space space space space equals 1 sin squared 15 degree plus sin squared 75 degree equals sin squared 15 degree plus sin squared open parentheses 90 degree minus 15 degree close parentheses space space space space space space space space space space space space space space space space space space space space space space space space equals sin squared 15 degree plus cos squared 15 degree space space space space space space space space space space space space space space space space space space space space space space space space equals 1 sin squared 20 degree plus sin squared 70 degree equals sin squared 20 degree plus sin squared open parentheses 90 degree minus 20 degree close parentheses space space space space space space space space space space space space space space space space space space space space space space space space equals sin squared 20 degree plus cos squared 20 degree space space space space space space space space space space space space space space space space space space space space space space space space equals 1 sin squared 25 degree plus sin squared 65 degree equals sin squared 25 degree plus sin squared open parentheses 90 degree minus 25 degree close parentheses space space space space space space space space space space space space space space space space space space space space space space space space equals sin squared 25 degree plus cos squared 25 degree space space space space space space space space space space space space space space space space space space space space space space space space equals 1 sin squared 30 degree plus sin squared 60 degree equals sin squared 30 degree plus sin squared open parentheses 90 degree minus 30 degree close parentheses space space space space space space space space space space space space space space space space space space space space space space space space equals sin squared 30 degree plus cos squared 30 degree space space space space space space space space space space space space space space space space space space space space space space space space equals 1 sin squared 35 degree plus sin squared 55 degree equals sin squared 35 degree plus sin squared open parentheses 90 degree minus 35 degree close parentheses space space space space space space space space space space space space space space space space space space space space space space space space equals sin squared 35 degree plus cos squared 35 degree space space space space space space space space space space space space space space space space space space space space space space space space equals 1 sin squared 40 degree plus sin squared 50 degree equals sin squared 40 degree plus sin squared open parentheses 90 degree minus 50 degree close parentheses space space space space space space space space space space space space space space space space space space space space space space space space equals sin squared 40 degree plus cos squared 40 degree space space space space space space space space space space space space space space space space space space space space space space space space equals 1 sin squared 45 degree equals open parentheses fraction numerator 1 over denominator square root of 2 end fraction close parentheses squared equals 1 half T h u s comma space w e space h a v e comma sin squared 5 degree plus sin squared 85 degree plus sin squared 10 degree plus sin squared 80 degree plus sin squared 15 degree plus sin squared 75 degree plus sin squared 20 degree plus sin squared 70 degree plus sin squared 25 degree plus sin squared 65 degree plus sin squared 30 degree plus sin squared 60 degree plus sin squared 35 degree plus sin squared 55 degree plus sin squared 40 degree plus sin squared 50 degree plus sin squared 45 degree plus sin squared 90 degree equals 1 plus 1 plus 1 plus 1 plus 1 plus 1 plus 1 plus 1 plus 1 half plus 1 equals 9 plus 1 half equals fraction numerator 18 plus 1 over denominator 2 end fraction equals 19 over 2

Answered by Vimala Ramamurthy | 28th Jun, 2015, 07:43: AM

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