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Question

# Find number of solutions of the equation ∣∣∣tan(|2x|+π3)∣∣∣=3 in (−π,π)

A
6
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B
8
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C
10
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D
4
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Solution

## The correct option is B 8As we know, number of solutions of equation ∣∣∣tan(|2x|+π3)∣∣∣=3 in (−π,π) is same as the number of points of intersection of y=∣∣∣tan(|2x|+π3)∣∣∣ and y=3 in (−π,π). Let's draw the graph of y=∣∣∣tan(|2x|+π3)∣∣∣. We can see, fundamental function involved here is tanx whose graph is given by Now apply the shrink along x-axis to y=tanx to get y=tan2x as shown below Further apply the modulus transformation to get y=tan|2x| as shown below, Now apply the horizontal shift to get y=tan(|2x|+π3) as shown below, Here we need to apply modulus flip along x-axis and we get the graph of y=∣∣∣tan(|2x|+π3)∣∣∣ as shown below Finally we need to draw y=3 and check the number of points of intersection in the graph We can see that there are 8 points of intersection in (−π,π). Hence the given equation have 8 solutions in (−π,π).

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