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

Question

The number of solutions of the equation $x+2	an x = \dfrac\pi2$ in the interval $[0,2\pi]$ is:

Accepted Answer

$$\tan x = \frac\pi4-\frac x2$$

Graphing $y=\tan x$ against the line $y=-\tfrac12x+\tfrac\pi4$ over $[0,2\pi]$ (across the branches of $\tan x$), the line intersects the tangent curve at 3 distinct points.

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