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If (1-cot 1^(@))*(1-cot2^(@))*(1-cot3^(@...

If `(1-cot 1^(@))*(1-cot2^(@))*(1-cot3^(@))...(1-cot44^(@))=2^(n)`, then `(n)/(11)` is equal to

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The correct Answer is:
2
If `(1-cot 1^(@))` ……………
`(1-cot 1^(!)) (1-cot 44^(@))`
`= 1 - cot 1^(@) - cot 44^(@)+cot 1^(@) cot 44^(@)` ……. (i)
Also `1 = cot (1^(@)+44^(@))= (cot 1^(@)cot 44^(@)-1)/(cot 1^(@)+cot 44^(@))`
`implies cot 1^(@)+cot 44^(@)=cot 1^(@) cot 44^(@)-1`
`implies 1=cot 1^(@)cot 44^(@) - cot 1^(@) - cot 44^(@)` ...... (ii)
from (i) and (ii) we get
`:. (1-cot 1^(@)) (1-cot 44^(@)) = 2`
similary `(1-cot 2^(@)) (1-cot 43^(@)) = 2`
`(1-cot 22^(@)) (1-cot 23^(@)) =2`
`:. (1- cot 1^(@)) (1-cot 2^(@))(1-cot 3^(@))....(1-cot 44^(@)) = 2^(22)`
`:. n = 22`
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