Question

The smallest positive root of the equation, tan x - x = 0 lies in

• A. $ \left(0, \frac{\pi}{2}\right) $
• B. $ \left(\frac{\pi}{2} , \pi \right) $
• C. $ \left(\pi , \frac{3\pi}{2}\right) $
• D. $ \left(\frac{3\pi}{2} , 2\pi \right) $
• E. None of these

Answer 1

Answer: (C)

It is clear from the graph that the curves y = tan x and y = x intersect at P in $(\pi,3 \pi / 2)$ .
Thus the smallest +ve root of tan x - x = 0 lies in $(\pi,3\pi / 2)$ .