How do you prove #tan^-1(1/4)+tan^-1(2/9)=tan^-1(1/2)#?

Question

4281 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-11-06T01:12:13

#LHS=tan^-1(1/4)+tan^-1(2/9)#

#=tan^-1((1/4+2/9)/(1-1/4xx2/9))#

#=tan^-1(((9*1+4*2)/36)/((36-2)/36))#

#=tan^-1((17/36)/((34)/36))#

#=tan^-1(cancel17/cancel36xxcancel36/cancel34^2)#

#=tan^-1(1/2)=RHS#

Proved