Prove that tan10+tan35+tan10.tan35=1

 Solution:- 

How to Prove:-

To prove tan10+tan35+tan10.tan35=1 we have to
known that tan45=1

=> 1=tan45
=> 1=tan(35+10)

replace tan(35+10) with tan(A+B) formula which is tanA+tanB/1-tanA.tanB
so equation becomes 
=> 1=tan35+tan10/1-tan35.tan10
=> 1-tan35.tan10=tan35+tan10
=> tan35+tan10=1-tan35.tan10
=>tan35+tan10+tan35.tan10=1

Hence L.H.S = R.H.S