Without using calculator or table of multiplication, show that #tan 195° = (sqrt3-1)/(sqrt3+1)#.?

Question

1367 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-04-11T02:24:36

#LHS=tan195^@#

#=tan(180^@+15^@)#

#=tan(15^@)#

#=tan(60^@-45^@)#

#=(tan60^@-tan45^@)/(1+tan60^@tan45^@)#

#=(sqrt3-1)/(1+sqrt3*1)#

#=(sqrt3-1)/(sqrt3+1)=RHS#