Prove that `(1+tan1^(@))(1+tan44^(@))(1+tan2^(@))(1+tan43^(@))………(1+tan22^(@))(1+tan23^(@))=2^(22)`.

Explanation

This is based on
`rArr tan(A+B) = (tanA+tanB)/(1-tanA.tanB)`
`tanA+tanB + tanA.tanB=1`
`rArr tanA+tanB+tanA.tanB+1=2`
`(1+tanA)(1+tanB)=2`
Using this
`(1+tanA)(1+tanB)=2`
Using this
`(1+tan1^(@))(1+tan44^(@))(1+tan2^(@))(1+tan43^(@))............(1+tan22^(@))(1+tan23^(@))`
Every two consecutive terms combine to give a value of 2 and there are 22 such pairs so its is equal to `2^(22)`.