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

1 Answer
May 28, 2018

See below

Explanation:

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