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The interval of a for which the equation...

The interval of `a` for which the equation `t a n^2x-(a-4)tanx+4-2a=0` has at least one solution `AAx in [0,pi//4]` `a in (2,3)` b. `a in [2,3]` c. `a in (1,4)` d. `a in [1,4]`

A

` a in (2,3)`

B

`a in [2, 3]`

C

` a in (1, 4)`

D

` a in [1 ,4]`

Text Solution

Verified by Experts

The correct Answer is:
2
`tan x = (a - 4 pm sqrt(a - 4)^(2) - 4 (4 - 2a))/(2)`
` = (a - 4 pm a)/(2) = a - 2 , - 2`
`therefore tan x = a- 2 ( because tan x ne - 2)`
` because a in [ 0 , (pi)/(4)]`
`because 0 le a - 2 le `
`rArr 2 le a le 3`
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