The number of solutions of the equation x + 2tanx = [ 2] in the interval [0, 2[]] is :

Question

The number of solutions of the equation x + 2tanx = $${\pi  \over 2}$$ in the interval [0, 2$$\pi$$] is :

Accepted Answer

$$x + 2\tan x = {\pi  \over 2}$$ in [0, 2$$\pi$$]

$$2\tan x = {\pi  \over 2} - x$$

$$\tan x = {\pi  \over 4} - {x \over 2}$$

$$y = \tan x$$ and $$y = {{ - x} \over 2} + {\pi  \over 4}$$

3 intersection points on the graph.

$$ \therefore $$ 3 solutions.

Solutions · 1