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