Question

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]`

Answer 1

Correct Answer - 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`