Unfortunately I have not found anything about the rules for this. Is there a way to simplify this?

Emery Boone

Emery Boone

Answered question

2022-05-23

Unfortunately I have not found anything about the rules for this. Is there a way to simplify this? Arctan ( a 2 ) Arctan ( b 2 )

Answer & Explanation

vikafa4g

vikafa4g

Beginner2022-05-24Added 15 answers

Since tan ( θ 2 + π 4 ) = sec θ + tan θ from Half-angle formulae, if we set a = a π 2 , and b = b π 2 , then we have:
sec a + tan a sec b + tan b
= csc a cot a csc b cot b
Since cot ( θ / 2 ) = csc θ + cot θ (from Half-angle formulae), we have:
cot ( a / 2 ) cot ( b / 2 )
= cot ( a / 2 ) tan ( b / 2 )
which is about as far as you can possibly get.

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