How do you verify #(2tan(x/2)) / (1+tan^2(x/2)) = sin x#?

Question

23602 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-09T19:54:53

See Below

#LHS : (2tan(x/2))/(1+tan^2(x/2))#

#=((2sin(x/2))/cos(x/2))/sec^2(x/2)#-> use the property #1+tan^2x=sec^2x#

#=((2sin(x/2))/cos(x/2))/(1/cos ^2(x/2))#

#=(2sin(x/2))/cos(x/2) * cos ^2(x/2)/1#

#=(2sin(x/2))/cancelcos(x/2) * cos ^cancel2(x/2)/1#

#=2sin(x/2)cos(x/2)#

#=sin2(x/2)#->use the property #sin2x=2sinxcosx#

#=sincancel2(x/cancel2)#

#=sinx#

#=RHS#