Tan20+tan40+tan60+..... Tan100=?

1 Answer
P dilip_k
Feb 19, 2018

#tan20+tan40+tan60+tan80+tan100#

#=(sin20/cos20+sin40/cos40)+sqrt3+tan80+tan(180-80)#

#=(sin20cos40+sin40cos20)/(cos20cos40)+sqrt3+tan80-tan80#

#=sin60/(cos20cos40)+sqrt3#

#=sqrt3/(2cos20cos40)+sqrt3#

#=(2sqrt3sin20)/(4sin20cos20cos40)+sqrt3#

#=(2sqrt3sin20)/(sin80)+sqrt3#

#=(4sqrt3sin10cos10)/sin(90-10)+sqrt3#

#=(4sqrt3sin10cos10)/cos10+sqrt3#

#=4sqrt3sin10+sqrt3#

Related questions
Impact of this question
3690 views around the world
You can reuse this answer
Creative Commons License