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Evaluate: inttan(x-theta)tan(x+theta)tan...

Evaluate: `inttan(x-theta)tan(x+theta)tan2x\ dx`

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To evaluate the integral \( \int \tan(x - \theta) \tan(x + \theta) \tan(2x) \, dx \), we can follow these steps: ### Step 1: Rewrite \( \tan(2x) \) We can express \( \tan(2x) \) in terms of \( \tan(x - \theta) \) and \( \tan(x + \theta) \). Using the angle addition formula for tangent, we have: \[ \tan(2x) = \tan((x - \theta) + (x + \theta)) = \frac{\tan(x - \theta) + \tan(x + \theta)}{1 - \tan(x - \theta) \tan(x + \theta)} \] ...
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Knowledge Check

  • inttan^(-1)((2tanx)/(1-tan^(2)x))dx=

    A
    `(x)/(2)+c`
    B
    `(x^(2))/(2)+c`
    C
    `x^(2)+c`
    D
    `2x^(2)+c`
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