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Adding inverse tangents with the compound-angle formula to evaluate a sum of three

Adding inverse tangents with the compound-angle formula to evaluate a sum of three

IB Year 6 | Grade 12
6 marks
  1. Given that \(\arctan\frac13+\arctan\frac17=\arctan k\), find the value of \(k\).[3]
  2. Hence find the exact value of \(2\arctan\frac13+\arctan\frac17\).[3]

Solution:

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Answer:(a) \(k=\frac12\) (b) \(\frac{\pi}{4}\)

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