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HPCET Tan Reduction — practice questions

Explore 1 free Tan Reduction questions in HPCET Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Tan Reduction questions and exercises with answers

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$\displaystyle\int_0^{\pi/4} \tan^4 x\, dx = ?$Read the answer and worked solution →

Worked practice questions

$\displaystyle\int_0^{\pi/4} \tan^4 x\, dx = ?$

  1. $\dfrac{\pi}{4} - \dfrac{2}{3}$
  2. $\dfrac{\pi}{4}$
  3. $\dfrac{1}{3}$
  4. $\dfrac{1}{3} - \dfrac{\pi}{4} + \dfrac{\pi}{2}$... — actually $\dfrac{3\pi - 8}{12}$ form
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Correct answer: A. $\dfrac{\pi}{4} - \dfrac{2}{3}$

**Reduction:** $I_n = \int_0^{\pi/4} \tan^n x\, dx$, $I_n + I_{n-2} = 1/(n-1)$. $I_0 = \pi/4$. $I_2 = 1 - \pi/4$. $I_4 = 1/3 - I_2 = 1/3 - 1 + \pi/4 = \pi/4 - 2/3$.

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