Question

Tan45*tan75*tan15*tan55*tan35=?

Answer 1

tan45*tan75*tan15*tan55*tan35
tan45*tan75*cot(90-15)*tan55*cot(90-35)
tan45*tan75*cot75*tan55*cot55

tan45=1
tan75*cot75=1 [tanx.cotx=1]
tan55*cot55=1

So the final answer is 1.

Answer 2

Tan45*tan75×tan(90-75)*tan55×tan(90-55)
1×tan75×cot75×tan55×cot55
1×Tan75×1/Tan75×Tan55×1/Tan55
1×1×1=1 Ans.
{Hints:- Tan(90-A)=CotA &TanA=1/CotA}