Verify: 2Arctan 1/2 = Arctan 4/3 ?

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Answer 1 · 2017-11-17T19:18:49

#2arctan(1/2)=arctan(4/3)#

Set #u=Arctan(1/2)#, so #tanu=1/2#

Hence #tan2u#

=#(2tanu)/[1-(tanu)^2]#

=#2*(1/2)/[1-(1/2)^2]#

=#1/(3/4)#

=#4/3#

Thus, #2arctan(1/2)=arctan(4/3)#