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Solve tan x=[x], x in (0, 3pi//2). Here ...

Solve `tan x=[x], x in (0, 3pi//2)`. Here [.] represents the greatest integer function.

Text Solution

Verified by Experts

The correct Answer is:
`x=tan^(-1) 4`
Graphs of `y=tan x` and `y=[x]` are drawn as shown in the following figure.

Clearly, `tan 1 gt tan (pi//4) or tan 1 gt 1`.
So, `y= tan x` and `y=[x]` do not intersect for `x in (0, pi//2)`.
Further from the figure, graphs intersect when `[x]=4`.
`:. tan x=4 or x=tan^(-1) 4`.
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