How to prove that $tan35+tan10+tan35tan10=1$ ?

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Answer 1 · 2018-05-28T09:21:49

See below

We use the identity

$tan(a-b)=(tana-tanb)/(1+tanatanb)$

And the fact $45=35-10$ . and $tan45=1$ . Then

$tan35=tan(45-10)=(tan45-tan10)/(1+tan45tan10)=$

$=(1-tan10)/(1+tan10)$ . Transposing terms, we have

$tan35(1+tan10)=1-tan10$

$tan35+tan35tan10+tan10=1$ QED

How to prove that tan35+tan10+tan35tan10=1tan35+tan10+tan35tan10=1?