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Floor Fulfilment (Posted on 2014-12-17) Difficulty: 3 of 5
Given that

    Σm = 1 to 44 cos mo
y = ---------------
    Σm = 1 to 44 sin mo

Find the value of floor(100y)

No Solution Yet Submitted by K Sengupta    
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p&p solution Comment 2 of 2 |

By regrouping the terms of the numerator we get: 

Σm = 1 to 44 cos m  =(2*cos(45/2)) *(cos(43/2)+ cos(41/2)+ cos(39/2)+… cos(1/2))  (i)


 

By the same reasoning:

 

Σm = 1 to 44 sin m     =(2*sin(45/2)) *(cos(43/2)+
cos(41/2)+ cos(39/2)+… cos(1/2))     (ii)

 

So:  y=cot (45/2 )

 

Since tan 45=1    and   tan 2x=2x/(1-x^2)  
 
cot (22.5)=1+sqrt(2)

 

Answer: floor 100*(1+sqrt(2)= 241

 


  Posted by Ady TZIDON on 2014-12-17 17:00:40
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