1.

If x in(1, 30) and (1+tan x^(@))(1+tan(x+1)^(@))...(1+tan(x+44)^(@)) = 2^(23) then value of x is

Answer»

`0`
`1`
`2`
`3`

Solution :If `x epsilon (1, 30)` and …………
`x = 1`
`(1+tan x^(@))(1+tan(x+1)^(@))…. (1+tan(x+44)^(@))ge(1+tan 1^(@))`
`(1+tan 2^(@)) ……….. (1+tan 45^(@))`
Now `(1+tan1^(@))(1+tan 44^(@))(1+tan2^(@))(tan 43^(@)+1)`………..
using `(1+tan x^(@))(1+tan(45-x^(@)))=2`
`(1+tan 1^(@))(1+tan 2^(@))............ (1+tan 45^(@)) = 2^(23)`


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