Question

Prove that the least positive value of `x ,` satisfying `tanx=x+1,l i e sint h ein t e r v a l(pi/4,pi/2)dot`

Answer 1

Let `f(x)=tan x " and " g(x)=x+1,` which can be shown as follows.

From the figure, `tanx =x+1` has infinitely many solutions but the least positive value of x lies in `((pi)/(4),(pi)/(2)).`