prove: tan10+tan70+tan100=tan10.tan70.tan100

Answer 1

Haven't tried it, but look at this:

https://answers.yahoo.com/question/index?qid=20150724191938AAydOpZ

sure looks messy, I am sure there is an easier way

Answer 2

100+70 = -10
Adding 'tan' on both sides,
tan(100+70)= -tan10
(tan100+tan70)/1-tan100.tan70 = -tan10
Multiplying 1-tan100.tan70 with -tan10,
tan100+ tan70= -tan10+tan10.tan100.tan70
tan10+tan100+tan70= tan10.tan70.tan100 proved

Answer 3

How 100-70=-10

Answer 4

100+70=170
So 100+10+70=180
170-180=-10