How to prove?

Question

Given that given #a=tan(b/2)#
prove that, #(2a)/((a^2)+1) = sin b#

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Answer 1 · 2018-02-22T18:49:51

See explanation

We want to verify the identity

#(2tan(b/2))/(tan^2(b/2)+1)=sin(b)#

We will use the identities

Thus:

#LHS=(2tan(b/2))/(tan^2(b/2)+1)#

#=(2tan(b/2))/sec^2(b/2)#

#=2tan(b/2)cos^2(b/2)#

#=2sin(b/2)/cos(b/2)cos^2(b/2)#

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

#=sin(b)=RHS#