Question

tan 5+tan 15+tan 25+......+tan 345+tan 355

Answer 1

tan 355 = tan (360 – 5) = - tan 5, tan 345 = tan ( 360 – 15 ) = -tan 15, tan 335 = tan (360 – 25 ) = -tan 25, tan 325 = tan ...

Answer 2

Tan5+Tan15+Tan25+.........+Tan345+Tan355

Tan (360-355)+Tan (360-345)+ Tan (360-335) +..........+Tan345+Tan355

-Tan355-Tan345-Tan335......Tan345+Tan355

Now all the terms are cancel and remain terns left are

Tan180

=0