What is the value of #(2tan(pi/12))/(1-tan^2(pi/12))#?

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Answer 1 · 2016-11-28T09:53:57

#(2tan(pi/12))/(1-tan^2(pi/12))=1/sqrt3#

As #tan(A+B)=(tanA+tanB)/(1-tanAtanB)#

if #A=B#, we have #tan2A=(tanA+tanA)/(1-tanAtanA)#

or #tan2A=(2tanA)/(1-tan^2A)#

Now putting #A=pi/12#

we have #(2tan(pi/12))/(1-tan^2(pi/12))=tan(2xxpi/12)=tan(pi/6)=1/sqrt3#

Answer 2 · 2016-11-28T09:55:53

Using identity #tan2theta=(2tantheta)/(1-tan^2theta)#

we have the Expression

#(2tan(pi/12))/ (1-tan^2(pi/12) )#

#=tan(2xxpi/12)=tan(pi/6)=1/sqrt3#