If the value of `cot(11 1/4^@)+tan(112 1/2^@)-cot(112 1/2^@)-tan(11 1/4^@)=sqrtn` where `n in N` then find the value of `n`

Answer

`2sqrt(2)`

Explanation

`cot(11(1^(@))/(4))+tan(112(1^(@))/(2))-cot(112(1^(@))/(2))-tan(11(1^(@))/(4))`
`=(cot11(1^(@))/(4)-tan11(1^(@))/(4))+tan(90^(@)+22(1^(@))/(2))-cot(90^(@)+22(1^(@))/(2))`
`=(2(1-tan^(2)11(1^(@))/(4)))/(2tan11(1^(@))/(4))-cot22(1^(@))/(2)+tan22(1^(@))/(2)`
`=2cot22(1^(@))/(2)-cot22(1^(@))/(2)+tan22(1^(@))/(2)`
`cot 22(1^(@))/(2)+tan22(1^(@))/(2)`
`=(sqrt(2)+1)+(sqrt(2)-1)`
`=2sqrt(2)`.