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x+2tanx=pi/2 Find the no. of values of x...

`x+2tanx=pi/2` Find the no. of values of x if `x in [0,2pi]`

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To solve the equation \( x + 2 \tan x = \frac{\pi}{2} \) for \( x \) in the interval \( [0, 2\pi] \), we will follow these steps: ### Step 1: Rearranging the Equation We start with the equation: \[ x + 2 \tan x = \frac{\pi}{2} \] Rearranging gives us: \[ 2 \tan x = \frac{\pi}{2} - x \] Dividing both sides by 2: \[ \tan x = \frac{\pi/2 - x}{2} \]
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