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How many solutions does the equation tan(2x) = tan(6x) have in the open interval (0, 3*pi)?

1. 4
2. 5
3. 6
4. 7

Correct answer: 7

Solution

From tan(2x) = tan(6x), we get 4x = n*pi so x = n*pi/4. We must exclude values where either tan(2x) or tan(6x) is undefined, then count valid x in (0, 3*pi).

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