Calculus

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Use the integral identity:
∫(a-1) (1/(1+x^2))dx=∫(1-1/a) (1/(1+u^2))du
for a>1 to show that:
arctan(a)+arctan(1/a)=π/2

  • Calculus -

    after the integration, you have

    arctan(1) - arctan(a) = arctan(1/a) - arctan(1)

    π/4 - arctan(a) = arctan(1/a) - π/4

    rearrange the terms and you're done.

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